MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY
MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY
MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY
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TEL-AVIV UNIVERSITY<br />
THE IBY AND ALDAR FLEISCHMAN FACULTY OF ENGINEERING<br />
<strong>MULTI</strong>-<strong>BEAM</strong> <strong>CYCLOTRON</strong>-<strong>RESONANCE</strong> <strong>MASER</strong> <strong>ARRAY</strong><br />
By<br />
Li Lei<br />
THESIS SUBMITTED FOR THE DEGREE OF “DOCTOR OF PHILOSOPHY”<br />
SUBMITTED TO THE SENATE OF TEL-AVIV UNIVERSITY<br />
February 2002
TEL-AVIV UNIVERSITY<br />
THE IBY AND ALDAR FLEISCHMAN FACULTY OF ENGINEERING<br />
<strong>MULTI</strong>-<strong>BEAM</strong> <strong>CYCLOTRON</strong>-<strong>RESONANCE</strong> <strong>MASER</strong> <strong>ARRAY</strong><br />
By<br />
Li Lei<br />
THESIS SUBMITTED FOR THE DEGREE OF “DOCTOR OF PHILOSOPHY”<br />
SUBMITTED TO THE SENATE OF TEL-AVIV UNIVERSITY<br />
This Research Work was Carried Out at Tel-Aviv University<br />
in The Faculty Of Engineering<br />
Under The Supervision of Prof. Eli Jerby<br />
February 2002<br />
II
This thesis is dedicated to my parents,<br />
Lei Mao-Fan and Yin Shou-Lan<br />
III
ACKNOWLEDGMENTS<br />
I would like to express my sincere gratitude to my advisor Prof. Eli Jerby for his help,<br />
guidance, encouragement and support, sharing with me his insights, knowledge and<br />
experience throughout this work.<br />
Particular thanks to Dr. A. Fisher and Dr. D. Hinshelwood from the Naval Research<br />
Laboratory for their help on the cathodes issue.<br />
A helpful and pleasant association with Mr. M. Korol, Mr. A. Shahadi, Mr. A. Kesar,<br />
Mr. M. Bensal and Mr. Y. Reshef at Tel-Aviv University over the years is also gratefully<br />
acknowledged.<br />
IV
Contents<br />
Abstract------------------------------------------------------------------------------------------VII<br />
List of Abbreviations---------------------------------------------------------------------------IX<br />
Chapter 1. Introduction 1<br />
1.1. Cyclotron Resonance Masers---------------------------------------------------1<br />
1.2. The Concept of the Multi-beam CRM-array---------------------------------12<br />
1.3. Electron Emitters----------------------------------------------------------------18<br />
1.4. Thesis Outline--------------------------------------------------------------------24<br />
Chapter 2. 2D CRM-Array Experiment 25<br />
2.1. Experimental Design and Setup-----------------------------------------------25<br />
2.1.1. Electron Beams-----------------------------------------------------------29<br />
2.1.2. Magnetic Fields----------------------------------------------------------32<br />
2.1.3. Pulsed Power Devices---------------------------------------------------34<br />
2.1.4. The Periodic Waveguide------------------------------------------------36<br />
2.1.5. Vacuum System Considerations---------------------------------------40<br />
2.1.6. RF Diagnostics-----------------------------------------------------------40<br />
2.2. Experimental Operation---------------------------------------------------------42<br />
2.3. Experimental Results------------------------------------------------------------44<br />
2.4. Analysis and Discussions-------------------------------------------------------55<br />
2.5. Conclusions-----------------------------------------------------------------------58<br />
Chapter 3. The Carbon-Fiber CRM-Array Experiment 59<br />
3.1. Experimental Design and Setup------------------------------------------------59<br />
3.1.1. Mechanical Design-------------------------------------------------------61<br />
3.1.2. Multi-beam Carbon-Fiber Cathode Arrays---------------------------64<br />
3.1.2.1. Experimental Configuration---------------------------------64<br />
3.1.2.2. Cathode Fabrications-----------------------------------------66<br />
3.1.2.3. Electron Trajectories------------------------------------------67<br />
V
3.1.2.4. Power Supplies -----------------------------------------------69<br />
3.1.2.5. Electrical Performance---------------------------------------72<br />
3.1.3. Magnetic Fields----------------------------------------------------------79<br />
3.1.4. The Periodic Waveguide------------------------------------------------81<br />
3.2. Experimental Operation---------------------------------------------------------84<br />
3.3. Experimental Results------------------------------------------------------------85<br />
3.4. Discussions-----------------------------------------------------------------------92<br />
Chapter 4. Conclusions 94<br />
4.1. Experimental Results------------------------------------------------------------94<br />
4.2. Suggestions for Future Work---------------------------------------------------95<br />
Appendix A. Computer Programs and Simulations Documentation 96<br />
A1. The EGUN Code Simulation for the 2D CRM-Array Experiment--------96<br />
A2. The Magnetic Fields Calculation for the 2D CRM-Array Experiment---99<br />
A3. The EGUN Code Simulation for the Carbon-Fiber CRM-array<br />
Experiment-----------------------------------------------------------------------101<br />
A4. The Magnetic Field Calculation for the Carbon-Fiber CRM-array<br />
Experiment-----------------------------------------------------------------------105<br />
Appendix B. Circuits of the Pulsed Power Devices 108<br />
B1. Circuit of the Gun-Solenoid Pulser-------------------------------------------108<br />
B2. Circuit of the Kicker Pulser---------------------------------------------------109<br />
B3. Circuit of the Multi-Channel Gun Pulser------------------------------------110<br />
Appendix C. The Modified Marx Generator 111<br />
C1. Model 615 MR Pulserad------------ ------------------------------------------111<br />
C2. The Modified Model 615 Pulserad-------------------------------------------112<br />
References 113<br />
VI
Abstract<br />
The cyclotron-resonance-maser array (CRM-array) proposed by Eli Jerby is a novel<br />
device in which separate electron beams perform, simultaneously, a cyclotron interaction<br />
with a single Bloch wave in an artificial lattice. It consists of CRM elements coupled<br />
together under a common magnetic field. The CRM-array has the capability to generate<br />
high-power microwave with relatively low-voltage electron beams. The low-voltage<br />
operation reduces the system overhead and leads to a relatively compact device. The<br />
CRM-array may radiate directly to free-space as an active phased-array antenna.<br />
Furthermore, the phase of each element output, and therefore the antenna far-field<br />
radiation pattern, can be varied by the electron-beam voltages.<br />
This thesis presents experimental studies of the multi-beam CRM-arrays. In the<br />
present study, our effort focuses mainly on the establishment of the experimental<br />
fundamental frame of the multi-beam CRM-arrays. In addition, a secondary objective of<br />
the research was to explore a multi-beam CRM device with cold cathode arrays and to<br />
develop an efficient, reliable and cost-effective multi-beam electron source for vacuum<br />
electronic devices. This thesis describes the first successful operation of a two-beam<br />
CRM-array experiment. The experimental results verify the feasibility of the CRM-array<br />
concept and promote the efforts toward the realization of large CRM-arrays.<br />
A 2D CRM array was operated with one and two electron beams (~ 10 keV / 0.1 A<br />
each). Microwave output signals are observed in frequencies around 7 GHz in an axial<br />
magnetic field of ~3 kG. Spectral measurements of the CRM outputs reveal frequency<br />
sweeps along the CRM pulses. These are associated with electron energy variations, in<br />
accordance with the theoretical CRM tuning condition. The synchronism of the cyclotronresonance<br />
interaction with a backward spatial harmonic is confirmed.<br />
This thesis presents also a first demonstration of a multi-beam CRM scheme with<br />
cold-cathode arrays. Based on commercial carbon fibers, a multi-beam cold-cathode array<br />
VII
demonstrates ~400 µs pulses of ~0.1 A in each channel with two accelerating stages. By<br />
using this gun, the device operates at low voltages ~5 kV with ~0.4 ms pulse duration.<br />
Clear bursts of RF oscillations were observed around 5 GHz in the experiment. The CRM<br />
tuning results indicate clearly interactions with backward waves. The experimental results<br />
show that it is possible to use cold-cathode arrays instead of thermionic-cathode arrays in<br />
future multi-beam CRM devices.<br />
VIII
List of abbreviations<br />
2D - Two Dimensions<br />
3D - Three Dimensions<br />
B.P.F - Bandpass Filter<br />
BWO - Backward Wave Oscillator<br />
CARM - Cyclotron Auto-Resonance Maser<br />
CsI - Cesium Iodide<br />
CRM - Cyclotron Resonance Maser<br />
EEE - Explosive Electron Emission<br />
FEL - Free Electron Laser<br />
Eq. - Equation<br />
H.P.F - High Pass Filter<br />
HPM - High Power Microwave<br />
IF - Intermediate Frequencies<br />
LO - Local Frequencies<br />
MBK - Multiple-Beam Klystron<br />
OBK - One-Beam Klystron<br />
PC - Personal Computer<br />
PWC - Periodic Waveguide Cyclotron Resonance Maser<br />
RF - Radio Frequencies<br />
SCR - Silicon Controlled Rectifier<br />
SF6 - Sulfur Hexafluoride<br />
TWT - Travelling Wave Tube<br />
IX
Chapter 1<br />
Introduction<br />
Driving by the emerged new technologies and the potential applications, the<br />
innovative high-power microwaves sources have been developed rapidly in recent years.<br />
This chapter describes the motivation for the present work on multi-beam cyclotron<br />
resonance maser arrays, and provides a brief review of relative fields. An outline of the<br />
thesis is presented in Section 1.4.<br />
1.1. Cyclotron Resonance Masers<br />
The cyclotron resonance masers (CRMs) [1] are the high power microwave sources,<br />
which are based on the induced cyclotron instability of a transiting electron beam. A<br />
simplified CRM scheme is shown in Fig. 1.1a. The electron beam is guided by a uniform<br />
axial magnetic field B0. Initially, the electrons undergo a cyclotron motion, and they are<br />
uniformly arranged in rotational phase on a circle (see Fig. 1.1b). Their Larmor radius is<br />
r0L=v0⊥/ωc, where v0⊥ is the electron initial perpendicular velocity, and ωc = eB0/γ0m0 is<br />
the cyclotron frequency. Here γ0=(1-v0 2 /c 2 ) -1/2 is the relativistic factor and m0 is the rest<br />
mass of the electron. After the interaction with the electromagnetic (em) field, some of the<br />
electrons are decelerated in the electric field, rotate faster, and hence accumulate phase<br />
lead while others are accelerated, rotate slower and accumulate phase lag. Then, a phase<br />
bunching occurs and the electrons radiate coherently. As the electrons gain or lose energy<br />
from the transverse electric field, the change in the relativistic factor γ0 produces a<br />
corresponding change in the cyclotron frequency. Simultaneously, another phase<br />
bunching process occurs due to the Weibel mechanism that is the result of the axial<br />
Lorentz force. The two processes are always operating against each other. The cyclotron<br />
resonance satisfies the condition:<br />
ω = n ω + k v<br />
(1.1)<br />
c<br />
1<br />
z<br />
z
E⊥<br />
ω, kz<br />
B0<br />
B⊥<br />
(a)<br />
E⊥<br />
(b)<br />
Fig. 1.1. The CRM interaction, (a) a schematic diagram, and (b) the process of the phase<br />
bunching (the white dots represent the electrons’ position at the time, t, and the red dots<br />
represent the electrons’ position at the time, t+∆t).<br />
2<br />
B0
where ω and kz are the em wave frequency and its wavenumber, respectively, ωc and vz<br />
are the electron cyclotron frequency and axial velocity, respectively, and n is the<br />
cyclotron harmonic order.<br />
In fast-wave devices, the phase velocity is higher than the speed of light in vacuum,<br />
vph>c, and the basic mechanism of radiation is the electron bunching under the influence<br />
of the transverse electric field component. The dominant effect in the fast-wave devices is<br />
the relativistic azimuthal bunching caused by the v⊥•E⊥ product, where v⊥ is the electron<br />
transverse velocity, E⊥ is the transverse electric component. In the slow-wave devices, the<br />
phase velocity is slower than the speed of light in vacuum, vph
CRMs have been developed and studied mainly in single electron-beam schemes [8].<br />
Fast-wave devices such as gyrotrons, cyclotron autoresonance masers (CARMs), and<br />
slow-wave devices such as dielectric-loaded CRMs have been studied intensively.<br />
Dispersion diagrams for gyrotrons, CARMs and dielectric-loaded CRMs are illustrated in<br />
Fig. 1.2. The uncoupled waveguide mode in Fig. 1.2a, b is represented by<br />
2 2 2 2<br />
ω = ω c 0 + k z c<br />
(1.3)<br />
where ω c0<br />
is the cutoff frequency of the operating mode. The cyclotron wave in the<br />
electron beam obeys Eq.1.1.<br />
Both gyrotrons and CARMs operate through a fast cyclotron wave interaction. For<br />
gyrotrons, the interaction takes place near the electron cyclotron frequency ωc (Fig. 1.2a)<br />
where the CARMs interaction takes places with a phase velocity closed to the speed of<br />
light, as shown in Fig. 1.2b. In Fig. 1.2c, the dispersion function of the uncoupled<br />
waveguide mode is determined by the geometry of the waveguide, its dielectric<br />
properties, the frequency ω, and the wavenumber k. The Weibel interaction takes place<br />
slightly below the speed of light line and the synchronism occurs over a wide bandwidth.<br />
Various CRMs are based on the normal Doppler effect. The resonance occurs when<br />
the operating frequency ω is larger than the Doppler term kzvz, which means that the<br />
phase velocity, vph= ω/kz , is larger than the electron axial velocity vz. This corresponds to<br />
positive cyclotron harmonics (n>0, see Eq. 1.1). The radiating electrons lose both orbital<br />
and axial momentum components. The anomalous Doppler effect occurs when the<br />
operating frequency ω is smaller than the Doppler term kzvz, i.e. vph
(a)<br />
(b)<br />
(c)<br />
Gyrotron interaction<br />
Waveguide mode<br />
Waveguide mode<br />
ωc<br />
ωc0<br />
ωc<br />
ωc<br />
Fig. 1.2. Dispersion diagrams for (a) gyrotrons, (b) CARMs, and (c) slow-wave CRMs.<br />
5<br />
ω<br />
ω<br />
Waveguide mode<br />
c<br />
c<br />
Fast cyclotron mode<br />
beam line<br />
CARM interaction<br />
Fast cyclotron mode<br />
beam line<br />
kz<br />
kz<br />
ω<br />
Slow wave CRM interaction<br />
Slow wave CRM interaction<br />
c<br />
Slow cyclotron mode<br />
beam line<br />
kz
A gyrotron system usually consists of several distinct elements: a magnetron injection<br />
gun, an interaction region, a collector region and a strong externally applied magnetic<br />
field [14]. The electron beam is emitted from the electron gun, propagates along the<br />
interaction region, interacts with the em wave, and is deposited finally in the collector.<br />
In the gyrotron device, the transverse velocity of electrons in a helical beam via<br />
relativistic instability generates the high power RF. The change of the electron cyclotron<br />
frequency due to the relativistic electron mass variation causes phase bunching in the<br />
electron beam and, consequently, electromagnetic cyclotron instabilities [15].<br />
Scientists at Gorky State University (former USSR) developed the gyrotron concept<br />
into a practical radiation source during the 60’s and 70’s. In 1975, they developed a 22<br />
kW CW oscillator that produced 2mm radiation with 22% efficiency [15]. In the 70’s<br />
there were also major advances in the United States at the Naval Research Laboratory<br />
(NRL) as well as at MIT, Yale University, Varian and Hughes.<br />
Gyro-devices, like linear-beam devices, have many variants. A full description of<br />
these devices is outside the scope of this work, but a list of the major types and schematic<br />
drawings of most important conventional linear-beam devices and their equivalent gyrodevices<br />
are presented in Table 1.1. For more detail see, for example Ref. [16].<br />
Existing or potential applications of gyro-devices include plasma heating and current<br />
drive for nuclear fusions, RF acceleration in high-energy linear colliders, enhanced radar<br />
systems, and processing of material [17]. In past several decades, common experimental<br />
features of gyro-devices are focused on high average-power gyrotrons and high peakpower<br />
pulsed gyrotrons.<br />
High average-power sources of 100-500 GHz radiations are necessary for electron<br />
cyclotron heating of fusion plasmas. The configurations of electron cyclotron masers with<br />
open quasi-optical resonators, such as the quasi-optical gyrotrons, show considerable<br />
promise for operation in this wavelength regime with high power RF.<br />
6
Cathode<br />
(a)<br />
Solenoid<br />
(b)<br />
(c)<br />
Electric field<br />
for TE01 mode<br />
Circular waveguide<br />
Fig. 1.3. Schematic diagrams of a gyrotron (a), the magnetic field<br />
profile (b) and the beam-cavity cross section in the interaction<br />
region for a circular TE01 operating mode (c) [Ref. 14].<br />
7<br />
B0z<br />
Collector<br />
Cavity<br />
Electron beam<br />
cross section<br />
z<br />
Typical electron<br />
cyclotron orbits<br />
RF output
In these configurations, the resonator mirrors are far from the beam-wave interaction<br />
region, which will allow a large volume for the interaction and low-ohmic heating<br />
densities on the mirrors. In addition, there is an effective control of transverse modes in<br />
the resonator, and separated electron-beam collection and RF output simplifies the<br />
development of depressed collectors. Table 1.2 presents a summary of the recent status of<br />
high frequency gyrotron oscillators for electron cyclotron resonance heating and current<br />
drive in nuclear fusion [18].<br />
Using a pulse-line accelerator, an early 1 GW super-radiant oscillator experiment was<br />
reported by Granatstein et al. at 8 GHz [19]. Since the late 1970’s, a number of significant<br />
experimental results were reported for relativistic gyrotrons in USSR. These experiments<br />
have yielded tens of megawatts peak power at centimeter and millimeter wavelengths<br />
regime. Recently, the whispering-gallery gyrotrons have produced several hundred<br />
megawatts peak power of microwaves near 35 GHz in the Naval Research Laboratory<br />
(NRL) [20].<br />
According to theoretical studies, gyrotrons may also have a high efficiency at high<br />
harmonics of the gyrofrequency. Thus interaction at high cyclotron harmonics becomes<br />
especially advantageous when large magnetic fields should be avoided [21]. At Fukui<br />
University, Japan and University of Sydney, Australia, the gyrotron have been operated<br />
successfully in single mode at the second and third harmonic of the electron cyclotron<br />
frequency [22-28]. The medium power and submillimeter gyrotron has achieved<br />
frequency tunability in a wide range, from 38 GHz to 850 GHz.<br />
Since the CARM was first suggested by Petelin [29] in 1974, several CARM<br />
experiments have been conducted at the Institute of Applied Physics in USSR [30-33],<br />
and at MIT [34, 35]. Recently, a CARM experiment with 26% high-efficiency at 7.9 mm<br />
wavelength was reported by Bratman et al. [36, 37]. Unlike the gyrotron, the CARM uses<br />
a large Doppler up-shift of the cyclotron frequency in order to reach high output<br />
frequencies [38, 39], and operates with vph~c.<br />
8
Table 1.1. Schematics of linear beam devices and corresponding gyro-devices [15].<br />
Linear<br />
beam<br />
devices<br />
Gyrodevices<br />
Monotron Klystron TWT BWO Twystron<br />
Gyro-<br />
Monotron<br />
Gyro-<br />
Klystron<br />
Table 1.2. Present development status of high frequency gyrotron oscillators [18].<br />
Frequency Power Period Efficiency<br />
Institution/State (GHz) (MW) (s) (%)<br />
CPI/US 110 0.68/0.53/0.35 0.5/2/10 31/30/27<br />
JAERI+Toshiba/Japan 110 0.35 5 30<br />
GYCOM/Russia 110 0.70/0.32 2/5 37/30<br />
Euratom Team/Europe 118 0.5/0.45 1/5 28/25<br />
GYCOM/Russia 140 1/0.65 1/2 >40<br />
GYCOM/Russia 140 0.8 1 50<br />
GYCOM/Russia 160 0.5 0.7 30<br />
JAERI+Toshiba/Japan 170 0.52/0.23 0.6/2.2 32<br />
9<br />
Gyro-<br />
TWT<br />
Gyro-<br />
BWO<br />
Gyro-<br />
Twystron
The CARM interaction is based on the same instability mechanism as that of the gyrotron,<br />
but it is operated much above cutoff frequency. The large Doppler frequency upshift<br />
permits a considerably reduced magnetic field B0. Therefore the CARM can provide<br />
millimeter and submillimeter radiation in the first electron-cyclotron harmonic using<br />
currently available magnet technology. In contrast to the gyrotron, which requires an<br />
electron beam with a large momentum pitch angle (typically α=v⊥/vz>1), the CARM has<br />
an electron beam with low to moderate pitch angle (α
unified description of CRM dynamics. This theory was further extended to the nonlinear<br />
range by Sprangle and co-workers [52, 53]. In 1980, Chu et al. applied kinetic theory to<br />
TE modes in cylindrical waveguides [54]. This method was extended later by Lau [55]<br />
and Fliflet [56] to TE and TM waveguide modes. The present status of the theory of<br />
cyclotron masers with relativistic electron beams is reviewed in [57].<br />
Azimuthal bunching<br />
V⊥•E⊥<br />
CRM devices<br />
Fast-wave devices Slow-wave devices<br />
CARM Gyrotron<br />
PWC Dielectric-loaded CRM<br />
Normal Doppler<br />
Vph>Vez<br />
Fig. 1.4. CRM effects and devices.<br />
11<br />
Axial bunching<br />
V⊥×B⊥<br />
Vph~c Vph>c Vph
1.2. The Concept of the Multi-beam CRM-array<br />
CRM devices have a number of potential scientific, industrial and military<br />
applications. In particular, they are expected to be widely used as major sources of HPMs<br />
in future applications, such as material processing, nuclear reactors, radars, accelerators,<br />
and others. CRM’s and gyrotrons have been developed so far as single electron-beam<br />
tubes. In order to obtain high output power, the sole electron-beam should possess<br />
sufficiently large kinetic energy and current. Consequently, a major part of the overhead<br />
in a typical CRM system is devoted to peripheral accessories needed to maintain the<br />
powerful electron-beam itself, both in acceleration and collector sections. In fact, most of<br />
the total length of a typical gyro-device is devoted to the consequent overhead (including<br />
the high-voltage electron gun and electron-optics, the tube shielding, a long collector, and<br />
the output window). Those contribute to weight and high cost. Therefore, the search for<br />
novel high-power microwave sources, which have low costs and compact sizes, is an<br />
attractive topic in this field.<br />
The concept of multi-beam CRM-arrays was proposed by Jerby et al. [58-60] as a<br />
compact version of the single-beam CRM schemes. The idea is based on employing the<br />
transverse dimension to reduce the requirements of high voltage supplies and cooling<br />
systems. In the CRM-array, separate electron beams perform, simultaneously, a cyclotron<br />
interaction with a single Bloch wave in an artificial lattice. The CRM-array has the<br />
capability to generate high-power microwaves with relatively low operating voltages.<br />
A theoretical analysis of the CRM-array [61, 62] predicts a considerable gain in a<br />
single mode. In this physical model, Maxwell’s equations and Vlasov equation are used<br />
to analyze the mechanism of the multi-beam CRM in the linear region. The multi-beam<br />
CRM-array gain-dispersion relation in Laplace s plane is given by the following matrix<br />
equation [61]<br />
2<br />
−1<br />
~ ^ ^ ^ ^<br />
^ ^ ^ 2<br />
1<br />
^ ^<br />
⎛ ⎞ ⎡ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎤ ⎛<br />
A⎜ s⎟<br />
= ⎢s⎜<br />
sU<br />
− Θ ⎟ − Qk<br />
⎜ s⎟C<br />
k ⎜ s⎟Θ<br />
pk ⎥ ⎜ sU<br />
− Θ k<br />
⎝<br />
⎠<br />
⎢⎣<br />
⎝<br />
⎞<br />
k ⎟<br />
⎠ 2 ⎝ ⎠ ⎝ ⎠ ⎥⎦<br />
⎝ ⎠<br />
12<br />
2<br />
A<br />
0<br />
(1.4)
^<br />
where the subscript k denotes the harmonic order, s= jsL(L<br />
is the interaction length) is<br />
the normalized Laplace wavenumber, and U is a unit matrix, respectively. The space-<br />
charge matrix Θ ^<br />
represents the effect of the electron current density on the CRM<br />
pk<br />
^<br />
coupling. The power-flow-matrix C<br />
⎛⎜<br />
k ⎝<br />
s<br />
⎞ ⎠ ⎟ describes the distribution of the em wave power<br />
among the different modes and their spatial harmonics. The diagonal tuning matrix is<br />
^<br />
Θ k<br />
^<br />
=θ nk<br />
^<br />
, where θnk − L<br />
=<br />
⎛⎜<br />
ω−ωc −βnk<br />
V<br />
⎞<br />
0z<br />
⎟<br />
⎝<br />
⎠<br />
V<br />
. The subscript n denotes the mode<br />
13<br />
−<br />
0z<br />
^<br />
order. Q<br />
⎛⎜<br />
k ⎝<br />
s<br />
⎞ ⎠ ⎟ is the diagonal coupling matrix and is defined as<br />
^ − ^ ^ ⎛ ^ −<br />
−<br />
⎛ ⎞ ⎛ ⎞<br />
⎞ 1<br />
^ ^ ^ ^<br />
2 ⎛<br />
⎞<br />
Q ⎜ ⎟ = ⎜ − Θ ⎟ ⎜ −<br />
⎟<br />
k s β ez sU<br />
k Z k β ez U + β e⊥<br />
⎜k<br />
0 Z k − sU<br />
− β k ⎟ (1.5)<br />
⎝ ⎠ ⎝ ⎠⎝<br />
⎠ 2 ⎝<br />
⎠<br />
^<br />
where k0 = kL is the normalized wavenumber, β ^<br />
k and Z ^<br />
k<br />
harmonic wavenumber and impedance, respectively, and β −<br />
are diagonal matrices of the<br />
ez<br />
and β−<br />
average normalized axial and perpendicular velocity components, respectively.<br />
e ⊥<br />
are the electron<br />
This linear analysis shows the possible mode selectivity and spectral purity of the 2D<br />
CRM-array. These stem from the spatial filtering in the periodic structure. In addition, the<br />
CRM-array may have unique features of an active phased array antenna [63]. The<br />
immediate integration proposed, of a microwave generator combined with an antenna,<br />
may simplify the overall radiative system in many applications.<br />
Other types of microwave generators with more than one electron-beam have been<br />
proposed and studied by other workers [64-76]. These include the multiple-beam klystron<br />
(MBK), the multi-beam stagger-tuned gyroklystron, and the double-stream cyclotron<br />
maser. Most of them are in the stage of theoretical study except MBK. Several<br />
experimental schemes are under construction.
The concept of the MBK appeared in France in the 40’s [64], and this kind of MBKs<br />
has really exploited in USSR. In recent years, MBKs are under consideration in other<br />
countries such as US and China. They have shown that the use of multiple-beam designs<br />
provides a powerful means for improving the parameters of microwave tubes. The MBKs<br />
provide low operating voltages, high power, low noise, and the possibility of wider<br />
operating bandwidth by the increase in total perveance. Many models of MBKs are<br />
produced in Russia and most of them for radar and communication applications.<br />
However, only a small number of them are widely known and few details were appeared<br />
in open publications [65]. According to Russian’s work, as the beam number grows, the<br />
decreases of the characteristic impedance of the resonator are slower than the increases of<br />
the overall conductance of the multiple-beam due to the smaller contribution of the side<br />
capacitance. Therefore, for a MBK and an OBK (one beam klystron), in the case of<br />
equality of beam powers, beam perveances, and normalized radii of the channels, the<br />
MBK bandwidth is 2-2.5 times more than that of the OBK [66]. Two 6 cavity, 36 beams<br />
MBKs produce a total RF output peak power of 500-1000 kW with 60A beam current and<br />
a 28-34 kV beam voltage at the State Research and Production Corporation “ISTOK” in<br />
Russia [67]. The MBKs at 0.425, 0.85, 1.3, and 2.8GHz are also under development at<br />
Thomson Tubes Electroniques [68, 69]. The 1.3 GHz prototype operates with seven 133<br />
A beams and a 115 kV beam voltage. It produces a total RF output peak power of 10 MW<br />
with 65% efficiency. Meanwhile, researchers in the Institute of Electronics, Chinese<br />
Academy of Sciences (IECAS) focus on S-band and C-band MBKs [70]. In US, under the<br />
MURI program, several progresses are carried out at Stanford Linear Accelerator Center<br />
and University of California, Davis. In a W-band micro-fabricated modular klystrons<br />
scheme, the semiconductor’s deep-etch lithography technique is used. A klystron array is<br />
fabricated on single substrate. Several such modules can be stacked together to form a<br />
klystron “brick” and operated in parallel in order to produce high power RF by relatively<br />
low voltage. The “brick” can be driven by a single output, or by individual, spatially<br />
combined radiators [71].<br />
Replacing the solid electron beams by hollow electron beams, a multi-beam<br />
gyroklystron was proposed by Nusinovich et al. A theoretical model of multi-beam<br />
14
stagger-tuned gyroklystrons was developed. Two-stage, two-, three- and four-beam<br />
gyroklystrons operating in a small-signal regime were considered in detail. The analysis<br />
shows that when a number of beamlets is greater than or equal to four, it is preferable to<br />
stagger tune eigenfrequencies of individual input cavities around the eigenfrequency of<br />
the common output cavity. The simulation results demonstrate that the gain-bandwidth<br />
product in multi-beam gyroklystrons can be increased due to the stagger tuning much<br />
more stronger than in their single-beam counterparts [72].<br />
The double-stream cyclotron maser was proposed by Bekefi at MIT [73]. In this<br />
scheme, two well-intermingled electron beams of different axial velocities are spun up<br />
and allowed to gyrate in a uniform axial magnetic field. The spun-up beams interact in a<br />
cylindrical waveguide. Bekefi’s formulae show that the resonant frequency of the<br />
cyclotron double-stream interaction is proportional to the cyclotron frequency and is<br />
inversely proportional to the difference in the axial velocities of the beams. He predicts<br />
that the double-stream cyclotron maser can operate at high frequencies without the need<br />
of either high-beam voltage or high magnetic field. Later, a linear instability analysis of<br />
this maser was developed by Bekefi and his co-workers and the result of computer<br />
simulations shows that the cyclotron two-stream instability is primarily electrostatic [74].<br />
A two-stream relativistic klystron amplifier and a high-power X-band relativistic twostream<br />
amplifier were proposed in a similar idea [75, 76]. The operating principle of these<br />
schemes is also based on the unstable interaction of the fast cyclotron space-charge wave<br />
on one electron beam and the slow cyclotron space-charge wave on other electron beam.<br />
The CRM-array was proposed by Jerby as an extension of the periodic-waveguide<br />
CRM scheme shown in Fig. 1.5a. In this device, referred here as a 1D CRM-array, the<br />
waveguide consists of metal posts in two columns, where the electron-beam flows in<br />
between them. Amplifier [46] and oscillator experiments [47] were conducted at X-band<br />
frequencies (8-12 GHz) with electron-beams of ~10 keV. The 1D-CRM oscillator yielded<br />
a coherent output of 0.4 kW power at >25% efficiency. Theoretical studies of 1D-CRM<br />
interactions with slow and fast waves are presented in [48]. A direct scale-up of this 1D<br />
scheme to high power levels might have required a system overhead comparable to that of<br />
15
similar single-beam gyrotrons. The preferred alternative was to increase the device<br />
dimensionality.<br />
Conceptual schemes of 2D and 3D CRM-arrays are illustrated in Figs. 1.5b and 1.5c,<br />
respectively. The CRM-array consists of many 1D CRM channels; each operates with a<br />
low-voltage, low-perveance electron beam. The different channels may be strongly<br />
coupled together through the waveguide lattice. Synergistic effects between these<br />
channels may increase the output power further. In order to compensate for any transverse<br />
non-uniformity in the magnetic field profile, each electron beam can be tuned to a slightly<br />
different accelerating voltage.<br />
The ultimate 3D CRM-array may consists of tens, and even hundreds electron beams.<br />
Advanced cathode arrays, made of carbon fibers, silicon tips, or ferroelectric ceramics,<br />
could be applicable in this device. The radiation output can be emitted from the exit plane<br />
of the CRM-array, directly to free-space. In more sophisticated schemes, the CRM-array<br />
may have features of an active phased-array antenna [63]. Focusing, steering, and<br />
splitting of the radiation lobe could be manipulated by varying the voltage profile across<br />
the cathode array.<br />
The major advantages expected for the CRM-array concept are:<br />
(a) Reduced power-supply size and weight.<br />
(b) Reduced X-ray radiation level due to the low-voltage operation.<br />
(c) Miniaturization due to the integrated magnet.<br />
(d) Reduced space-charge effects due to the separated low-current electron beams.<br />
(e) Spectral purity and mode selectivity determined by the lattice dispersion.<br />
(f) Direct radiation to free-space.<br />
(g) Direct energy radiation as a phased-array antenna, incorporated in the multi-beam<br />
CRM-array itself.<br />
The comparison of the single-beam high-power microwave source and the multi-beam<br />
CRM-array is summarized in Fig. 1.6.<br />
16
(a)<br />
(b)<br />
(c)<br />
B0<br />
B0<br />
B0<br />
metallic tube<br />
electron beam<br />
17<br />
electron beams<br />
metallic tube<br />
electron beams<br />
metal posts<br />
metal posts<br />
metallic tube<br />
metal posts<br />
Fig. 1.5. The evolution of the CRM-array concept: 1D, 2D, and 3D<br />
CRM-array schemes (a, b and c, respectively).
1.3. Electron Emitters<br />
There are several kinds of cathodes used in high power microwave devices. The most<br />
common cathodes are thermionic cathodes. Cold cathodes are also used. In this work we<br />
utilize both thermionic cathodes and cold cathodes.<br />
Thermionic Cathodes<br />
HPM Generation<br />
Single high energy e-beam Multi-beam CRM-array<br />
High voltage<br />
Large system overhead<br />
Need X-ray shielding<br />
High current<br />
Space charge effects<br />
Increase the spatial dimension<br />
Fig. 1.6. Single-beam vs. multi-beam HPM generation.<br />
Thermionic cathodes are based on thermionic emission mechanisms. Thermionic<br />
emission results from the heating of the cathode to provide the electrons with a sufficient<br />
kinetic energy to overcome the potential barrier (work function) at the surface and escape<br />
18<br />
Array of low-voltage<br />
Compact size, less X-ray<br />
Separated electron beams<br />
Less space charge effects<br />
Lattice dispersion<br />
Mode selectivity<br />
Beam steering<br />
“Active” phased array
into vacuum. The current density J is given by the Richardson-Dushman equation as<br />
follows [77]:<br />
2 ⎛ eφ<br />
⎞<br />
J = A0<br />
T exp⎜−<br />
⎟ A/cm<br />
⎝ kT ⎠<br />
2 (1.6)<br />
where k is the Boltzmann constant, φ is the work function, T is the absolute temperature<br />
in degrees Kelvin ( o K), and A0 = 1.20×10 6 A/cm 2 o K 2 .<br />
However, in the case of space charge limitation, the current density J is given by the<br />
Langmuir-Child equation [78, 79]<br />
−6<br />
3 / 2<br />
J = 2. 3×<br />
10 GV A/cm 2 (1.7)<br />
where V is the acceleration voltage in volts, and G is a quantity, given in cm -2 , which<br />
depends on the geometric configuration of the electrodes. In the simplest case of parallelsided<br />
electrodes, G=1/d 2 , d is the cathode-anode distance. From Eq. 1.6, it is clear that in<br />
order to obtain a strong emission, the work function φ must be low and the temperature<br />
Τ must be high. Because Barium has a low work function (1.8 eV) and a moderate<br />
melting temperature (850 0 C), Barium impregnated tungsten cathodes have been widely<br />
studied since their introduction in the early 50’s. The Philips B-type cathode developed<br />
by Levi [80, 81] in 1953 is still the most widely used cathode in the microwave tube<br />
industry. An improved version of the familiar impregnated cathode is the M-cathode [82],<br />
which employs a coating of an ally of platinum group metals on the emissive surface to<br />
lower the work function of the activated cathode. Then this emitter may be operated at<br />
lower temperatures than the standard dispenser cathode for the same current density and<br />
has significantly longer operating lifetime. More recently, new types of cathodes have<br />
been investigated, for instance, a variety of versions of the impregnated dispenser cathode<br />
is distinguished by the composition of the impregnation or by the substrate type [83].<br />
Cold Cathodes<br />
The current density of conventional thermionic cathodes is limited to the order of 10<br />
A/cm 2 [84]. For ultra high power microwave generation, a larger current density is<br />
required. In addition, direct modulation of the emitted beam can improve the efficiency<br />
19
and reduce the size of the microwave source. Thus various cold cathodes have been<br />
developed over the years to meet those desires.<br />
Cold cathodes do not rely on the heating of a material to emit electrons over the<br />
potential barrier. One of the most common types of cold cathodes is the field emitter,<br />
which is based on field emission. Field emission is the process whereby electrons tunnel<br />
through a barrier in the presence of a high electric field. Fowler and Nordheim developed<br />
a model describing the emission of electrons from a metal-vacuum interface in the<br />
presence of an electric field normal to the surface [85]. Their theory predicted that the<br />
current density of the field emission can be expressed as<br />
C<br />
J = 2<br />
φt<br />
( y)<br />
E<br />
2<br />
3 ⎛<br />
⎜ 2 Bφ<br />
v<br />
exp⎜<br />
−<br />
⎜ E<br />
⎝<br />
20<br />
( y)<br />
⎞<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
A/cm 2 (1.8)<br />
where E is the applied electric field, φ is the work function, C and B are constants,<br />
3 2<br />
y = e E φ , and v(y) and t(y) are tabulated functions which arise due the inclusion of<br />
image charge effects.<br />
Dyke and Dolan have recognized the advantages of field emission as a highbrightness<br />
electron source in the 50’s. They discovered that to ensure stable emission and<br />
long life on tungsten field emitters, the ultra-high vacuum is required [86]. Later, the<br />
group at Stanford Research Institute (SRI), lead by Spindt, has developed the gated field<br />
emitter arrays (FEAs) successfully using micro-fabrication technology [87]. The Spindttype<br />
FEAs become one of the most common structures for field emission cathodes. The<br />
“Spindt cathode” is illustrated in Fig. 1.6. In the Spindt structure, the electrons are<br />
generated from very sharp molybdenum tips and an electron gate electrode is used to low<br />
the necessary operating voltage in order to produce a large electric field at the tips.<br />
Despite the variety of techniques and material, this kind of FEAs has been developed<br />
successfully as commercial flat panel displays, field emission displays (FEDs). Since<br />
FEDs have almost 180 degrees viewing angle, excellent color reproduction, flatness and<br />
low power consumption, it looks very promising.
There are many other types of cold cathodes, such as photocathodes, ferroelectric<br />
ceramic cathodes and explosive electron emission cathodes. We will describe more in<br />
detail the latter one in the following sections since this work has used carbon-fiber<br />
cathodes. For more details on other cathodes see, for example, the review article by<br />
Nation et al. [88].<br />
Vanode<br />
Vgate<br />
Fig. 1.6. Schematic of Spindt-type field emitter array.<br />
Compared with field emitters, when the electric field is high enough, ohmic heating of<br />
the discrete electron emission sites will explode the cathode to vaporize and subsequent<br />
plasma formation by electron neutral collisions. There is also plasma formation on the<br />
anode, and diode gap closure occurs as the two plasma fronts expand. This process is<br />
known as explosive electron emission [88].<br />
In USSR, Mesyats’ group has made since the mid 1960’s an extensive research on the<br />
processes of plasma formation and intense electron beams involved microscopic point<br />
emitters at high current densities emission. According their report, the work behavior of<br />
the explosive single emitter has four stages [89, 90]. Initially, followed a rapid rise in<br />
current a field emission current is observed after some delay by an explosive destruction<br />
21<br />
Anode<br />
micro tip<br />
gate electrode<br />
substrate
of the emitter. Simultaneous with the beginning of the current rise, a cathode flare appears<br />
on the cathode. Then, the current rises slowly, which is attributed to a decrease in the<br />
impedance due to plasma expansion. Later, an anode flare appears and the diode<br />
impedance collapses, simultaneous with a rapid current increase. The breakdown time,<br />
τδ , is related to the plateau current, j, by j 2 τδ=constant. Here j strongly depends on the<br />
electric field, so does τδ . If the explosion is initiated by field-emission current, the<br />
Fowler-Nordheim equation gives a good agreement with these single emitter experiments.<br />
Focused on broad area cathodes, Parker and coworkers at the Air Force Weapons<br />
Laboratory studied in the 70’s the electrical behavior of graphite cathodes. They<br />
considered that the observed diode perveance can be explained in terms of the expansion<br />
of the plasma cathode formed by the merger of many cathode flares [91]. The exact<br />
mechanism for broad area cathodes is not yet known; none of the theories so far proposed<br />
can explain all of the experimental results. However, the pre-breakdown and breakdown<br />
currents in a broad area cathode are observed to occur at electric fields about 10-1000<br />
times lower than those in a single needle emitter [92]. The effect of gap closure may limit<br />
the performance of devices operating with cold-cathodes, since it limits the duration of<br />
the electron-beam pulse, and precludes operation at desired repetition rates [93].<br />
Impedance collapse characterized by the speed of the gap closure is roughly constant over<br />
a wide range of conditions at values of about 10 6 cm/s. Because of the gap closure, most<br />
of the cathodes used limit the pulsed duration to about 100’s ns. In order to prevent the<br />
breakdown, most studies in the cold cathodes use short pulse. It is useful, therefore, to<br />
develop new kinds of cold cathodes or processes, which the pulse lengths can be<br />
extended.<br />
Recently, the researchers at NEC Corporation in Japan have demonstrated a<br />
miniaturized traveling waveguide tube (TWT) results of 27.5 W at 10.5 GHz, 19.5 dB<br />
gain, and a bandwidth wider than 3 GHz using a lateral-resistor-stabilized Spindt-type<br />
FEAs [94]. Another TWT design by NEC, using a new arc-resistant vertical current<br />
limiter Spindt-type FEAs resulted an 8 W output power, 22 dB gain at 11.5 GHz and was<br />
stably operated for 5000 hours [95, 96]. The arc-resistant FEA appears to dramatically<br />
22
enhance the lifetime of the FEA cathodes in the vacuum environment and re-energize the<br />
efforts of researchers to develop high-power vacuum electronic devices based on cold<br />
cathodes.<br />
Carbon fibers are known for a long time as field emission sources [97-99]. In these<br />
early works, carbon fibers have been studied as pure field emitters, having been used<br />
singly and in clusters to provide DC emission without plasma formation. The<br />
experimental results have a good agreement with the Fowler-Nordheim equation. The<br />
emission characteristics and stability of these cathodes are, to a large degree, determined<br />
by the type of the carbon fiber microstructure, by the features of the manufacturing<br />
process, and by the initial treatment of the emitters.<br />
Further developments of carbon-fiber emitters with plasma formation in western<br />
countries were reported in the 80’s by Prohaska and Fisher. Using carbon yarn, emission<br />
starts at 5-15kV/cm and 10-30kV/cm, current densities up to 10A/cm 2 have been obtained<br />
over 100 cm 2 [100]. Researchers in New Mexico demonstrated that cloth fiber (75%<br />
rayon, 25% silk) cathodes might have superior properties as cold cathode emitters [101].<br />
However for the broad area carbon-fiber emitters, the experimental results do not agree<br />
with the Fowler-Nordheim equation. Even with extremely careful diode design, the<br />
available pulse duration for any of the carbon felt, velvet, and high-grade graphite<br />
cathodes is usually limited by gap closure. The gap closure velocity depends most<br />
critically on the electrical field strength at the cathode surface, the cathode emissive<br />
material, and magnetic field [102]. Most recently, experiments on carbon-fiber emitters<br />
have tested the effect of CsI (Cesium Iodide) coated carbon-fiber cathodes [103, 104].<br />
They have found that carbon-fiber cathodes coated with CsI did reduce the speed of the<br />
gap closure. In our laboratory, the single beam carbon-fiber cathode was demonstrated for<br />
1.2 ms current pulses [105], and was operated for a CRM experiment [106].<br />
The carbon-fiber cathode is rarely used in microwave-tube experiments [107]. Since<br />
carbon has a high sublimation temperature (4×10 3 0 K), it has a long lifetime at current<br />
densities of >10 3 A/cm 2 [103]. In addition, such kind of material can easily be configured<br />
23
to provide multi electron beams in arbitrarily large diameter configurations. Therefore, in<br />
this study we use carbon-fiber cathodes to explore the operation of multi-beam coldcathode<br />
arrays for the CRM devices.<br />
1.4. Thesis Outline<br />
The thesis describes the experimental studies of the multi-beam CRM-arrays. At<br />
present, our studies focus mainly on the establishment of the experimental fundamental<br />
frame of the multi-beam CRM-array. A secondary objective is to explore multi-beam<br />
CRM devices based on the cold-cathode arrays, carbon-fiber cathode arrays, and to<br />
develop an efficient, reliable and cost-effective multi electron-beam source.<br />
In this thesis, Chapter 2 presents the first successful operation of a two-beam CRMarray.<br />
The spectral measurements were carried out with one and two-electron beam CRM<br />
devices. The chapter includes a detail description of the experimental setup, experimental<br />
operation, experimental results, and an analysis of the possible mechanism for the<br />
resonant microwave radiation observed. The first carbon-fiber CRM-array experiment is<br />
presented in Chapter 3. The multi-beam CRM scheme with cold-cathode arrays is<br />
demonstrated. This experiment illustrates the use of carbon-fiber emitters as electron<br />
sources in multi-beam CRM devices. Meanwhile, the study of the multi-beam carbonfiber<br />
cathode array is described intensively in this chapter. The conclusions of this thesis<br />
are summarized in Chapter 4.<br />
24
Chapter 2<br />
2D CRM-Array Experiment<br />
This chapter presents the first experimental study of a 2D CRM-array. The CRMarray<br />
operates with one or two electron beams. The next section describes the<br />
experimental design and setup. The operation of the experiment is described in Section<br />
2.2. The highlights of the experimental results in each case are presented in Section 2.3.<br />
Both, fast- and slow-wave CRM interactions are observed in the experiment. The spectral<br />
measurements show clearly the CRM interaction with backward spatial harmonics. The<br />
experimental results are analyzed and compared to the theory in Section 2.4. The<br />
conclusions are presented in Section 2.5.<br />
2.1. Experimental Design and Setup<br />
A photograph of the experimental setup of the 2D CRM-array is shown in Fig. 2.1.<br />
The oscillator tube consists of a planar multi-beam electron gun, a 2D periodic<br />
waveguide, a collector, a solenoid, and a kicker coil, which imparts initial transverse<br />
velocity to the electrons. The total length of the system is about one meter.<br />
A block diagram of the experimental setup is shown in Fig. 2.2. The CRM device is<br />
immersed in a uniform axial magnetic field (2-4 kG) and activated by pulsed power<br />
supplies. The electron beams are emitted from dispenser thermionic cathodes (Spectra-<br />
Mat, STD200, 5 mm diameter), spun up by the small kicker coil, and propagate in<br />
cyclotron motions along the periodic waveguide channels. The waveguide consists of a<br />
metal-post array with 4x24 elements and is terminated by half-period reflecting sections<br />
in both ends. The first row of metal posts acts as an anode. A waveguide taper at the end<br />
is used as a mode converter and also as a collector for the electron beams. In another<br />
scheme (not presented here) the collector is divided to each electron beam. The beam<br />
currents are measured by means of 10 Ω resistors. A small portion of the RF power is<br />
sampled by a 20 dB cross-coupler, and by three sampling probes mounted inside the<br />
25
waveguide. The output coupled RF signal is attenuated and divided into two arms. In one<br />
arm, the signal is detected by a high-sensitivity crystal detector and recorded by a digital<br />
oscilloscope (Tektronix TDS 540). In the other arm, the signal is fed into a mixer (HP<br />
5364A) and mixed with a local-oscillator wave generated by a synthesizer (HP 83752A).<br />
The heterodyne signal is analyzed by a frequency and time-interval analyzer (HP 5372A),<br />
which enables intra-pulse frequency variation measurements. The parameters of the 2D<br />
CRM-array experiment are listed in Table 2.1. The more detail design is given in the<br />
following sections.<br />
Fig. 2.1. Photograph of the experimental setup.<br />
26
electron<br />
gun<br />
vacuum pump<br />
pulsers RF diagnostics<br />
kicker<br />
solenoid<br />
Fig. 2.2. Schematic of the 2D CRM-array experimental setup.<br />
27<br />
Frequency-time<br />
analyzer<br />
synthesizer<br />
RF probes<br />
cathodes waveguide solenoid<br />
mixer<br />
attenuators<br />
oscilloscope<br />
detector<br />
10Ω<br />
RF coupling<br />
Collector<br />
and RF-load
Table 2.1. 2D CRM-array Experimental parameters.<br />
Electron beams:<br />
energy 4.0 - 10.5 keV<br />
beam current ~ 0.1 A<br />
pulse duration 0.2 ms<br />
beams 1 or 2<br />
Magnetic fields:<br />
solenoid 2.5 - 3.9 kG<br />
kicker ~ 0.7 kA turns<br />
Periodic waveguide:<br />
rectangular tube 48 × 22 mm 2<br />
length 48 cm<br />
post diameter 1.5 mm<br />
array size 4 × 24<br />
periodicity 20 mm<br />
28
2.1.1. Electron Beams<br />
A planar electron gun was used in this experiment. A sketch of the electron gun is<br />
shown in Fig. 2.3. In the two-beam CRM experiment, the two side cathodes shown in red<br />
color in Fig. 2.3 were used to generate electron beams; whereas, in the one-beam CRM<br />
experiments, all of them were used separately to generate an electron beam in individual<br />
experiment. The gap between anode and cathode is 6 mm. A 2 mm thick stainless steel<br />
was used to fabricate the anode. The anode has three 6 mm diameter holes in order to<br />
apply the multi-beam operation. The distance between two adjacent cathodes is 9.5 mm.<br />
The cathodes are STD200 dispenser thermionic cathodes (5 mm diameter) made by<br />
Spectra-Mat Ltd. In a later experiment, for the vacuum consideration, we removed this<br />
anode and used the first row of metal posts in the periodic waveguide as an anode. For a<br />
new cathode, the optimal filament voltage is approximately 8V and the heating power is<br />
around 40 W.<br />
cathodes<br />
Fig. 2.3. Sketch of the electron gun used in the 2D CRM-array experiment.<br />
The electron gun design was performed with the EGUN code [108] with a few<br />
assumptions. This code is designed to compute trajectories of charged particles in a 2D<br />
symmetry of electrostatic and magnetostatic fields, including the effects of space charges<br />
and self-magnetic fields. Starting options include Child’s Law conditions on cathodes of<br />
various shapes, as well as user specified initial conditions. In the 2D CRM-array<br />
experiment, we assumed: (1) each beam has a perfect local symmetry around its own<br />
axis, (2) each beam has the same electron flow, (3) the gap between cathode and anode is<br />
smaller than the distance between two holes in the anode.<br />
29<br />
anode<br />
cathode holder
R (mm)<br />
Current Density (0.0246 A/mm 2 )<br />
Fig. 2.4. The EGUN code output for a 5mm cathode and 6mm gap with a tapered magnetic<br />
field: (a) the beam trajectory [radius (R) vs. axial length (Z)], (b) electron density vs.<br />
radius (R).<br />
30<br />
Z (mm)<br />
R (mm)
Fig. 2.4. (Cont.) The EGUN code output for a 5mm cathode and 6mm gap with a tapered<br />
magnetic field: (c) the angle of the electron motion measured from the z axis.<br />
Thus we simulated the center electron flow and simplified the boundary. The code output<br />
for a 5 mm cathode with 6 mm gap is shown in Fig. 2.4. Fig. 2.4a shows electron gun<br />
geometry and beam trajectory. It includes two regions: a cathode-anode region and a<br />
beam tunnel. Figs. 2.4 b, c presents electron density versus radius, and the angle of the<br />
electron motion measured from the z-axis.<br />
31<br />
R (mm)
2.1.2. Magnetic Fields<br />
In this experiment, we used a solenoid to provide an axial magnetic field for<br />
cyclotron motions. It was made out of a 2 mm diameter copper wire with 15 turns/cm.<br />
Similarly, a kicker was made out of a 1 mm diameter copper wire with 52 turns/cm. The<br />
cross section view of a round, finite, air core solenoid is shown in Fig. 2.5.<br />
by<br />
B<br />
z<br />
The magnetic field at any point on the axis of a finite solenoid is approximated [109]<br />
⎧<br />
⎪<br />
µ NI<br />
r +<br />
⎪⎛<br />
⎞<br />
=<br />
0<br />
l 2<br />
( z)<br />
k<br />
⎨⎜<br />
z + ⎟ ln<br />
2(<br />
r − r ) l ⎪⎝<br />
2<br />
2 1<br />
⎠<br />
⎪ r +<br />
⎪<br />
1<br />
⎩<br />
2<br />
2 ⎛ l ⎞<br />
r + ⎜ z + ⎟<br />
r +<br />
2 ⎝ 2 ⎠ ⎛ l ⎞ 2<br />
− ⎜ z − ⎟ ln<br />
2 ⎝ 2 ⎠<br />
2 ⎛ l ⎞<br />
r + ⎜ z + ⎟<br />
r +<br />
1 ⎝ 2 ⎠<br />
1<br />
where Bz is the magnetic field, in Tesla, µ0 is the permeability constant (1.26×10 -6 H/m,<br />
for coils measured in meters). Ik is the current in Amperes. l, r1, r2, and N are the<br />
solenoid length, inner and outer radii, and the number of turns, respectively, The<br />
experimental parameters are shown in Table 2.2. In Fig. 2.6, the solid curve shows the<br />
magnetic field of the solenoid and the dashed curve shows the magnetic field of the<br />
kicker. The star sign indicates the front-end position of the cathodes.<br />
r2 r1<br />
Fig. 2.5. Solenoid in cross section.<br />
l<br />
32<br />
2 ⎫<br />
2 ⎛ l ⎞<br />
r + ⎜ z − ⎪<br />
2<br />
⎟<br />
⎝ 2 ⎠ ⎪<br />
⎬<br />
2<br />
2 ⎛ l ⎞ ⎪<br />
r + ⎜ z −<br />
1<br />
⎟ ⎪<br />
⎝ 2 ⎠ ⎪⎭<br />
z B<br />
(2.1)
Table 2.2. The parameters of the solenoid and the kicker.<br />
Parameter Solenoid Kicker<br />
Turns 900 120<br />
Current [A] 100-200 20-140<br />
Inner radius r1 [cm] 5.15 5.5<br />
Outer radius r2 [cm] 6.3 6.5<br />
Length l [cm] 60 2.3<br />
*<br />
Fig. 2.6. The magnetic fields of solenoid (solid curve) and kicker (dashed curve).<br />
The star sign represents the start point of the electron beam.<br />
33
2.1.3. Pulsed Power Devices<br />
Three high-voltage pulsers were designed and built in order to run the CRM<br />
experiment. The three incorporate pulsers are used for the electron gun, solenoid, and<br />
kicker. Their electric circuits are shown in Appendices B1 and B2. An overview of the<br />
pulsers is shown in Fig. 2.7. Each of the pulsers consists of a low-voltage capacitor bank<br />
(C), an SCR control circuit which is used as a gate, a diode Dc which prevents a reverse<br />
recharging of the capacitor, and a transformer (car ignition coil). Fig. 2.8 shows<br />
schematically a principle configuration of a high voltage electron gun pulser [110]. In<br />
this scheme an electron gun serves as a load. The high-voltage secondary winding of the<br />
transformer is connected directly to the electron gun. The pulse length, the voltage, the<br />
maximum currents, and the load’s parameters determine the parameters of each pulser.<br />
Fig. 2.9 shows schematically a principle configuration of a high voltage solenoid pulser.<br />
Here high voltage comes out from charged capacitors directly. The homemade solenoid<br />
pulser generates a 650 V, 40 ms pulse that corresponds to a peak magnetic field of 3 kG.<br />
The electron gun pulse reaches 12 kV and its pulse width is around 0.4 ms. The kicker<br />
coil can produce 7 kG maximum magnetic field on axis. All three pulsers are triggered<br />
with an adjustable delay between them. The kicker and electron gun pulsers are triggered<br />
near the peak of the solenoid pulse as shown in the timing diagram in Fig. 2.10. The<br />
solenoid pulse has 40 ms duration. Comparing to the 0.4 ms duration of the electron gun<br />
pulse, the CRM operates in a closely constant magnetic field. The electron gun voltage is<br />
measured by a high voltage probe (Tektronix P6015A). The currents of the solenoid and<br />
the kicker are measured with a series 0.05 Ω resistors.<br />
Fig. 2.7. Overview of the homemade pulsers.<br />
34
control<br />
control<br />
Voltage [a.u]<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
SCR<br />
C<br />
Dc<br />
Fig. 2.8. Schematic of the electron gun pulser.<br />
SCR<br />
Dc<br />
Fig. 2.9. Schematic of the solenoid pulser.<br />
Gun<br />
-10 -5 0 5<br />
Time [ms]<br />
10 15 20<br />
35<br />
Kicker<br />
Solenoid<br />
Fig. 2.10. A timing diagram of the solenoid, kicker and electron<br />
gun pulsers.<br />
cathode<br />
electron gun<br />
solenoid<br />
anode
2.1.4. The Periodic Waveguide<br />
The periodic waveguide used in this experiment is illustrated in Fig. 2.11. The main<br />
part is a 60 cm long WR 187 waveguide welded with a 4×24 metal-post array. It is<br />
terminated by half-period reflecting sections in both ends. The first row of metal posts<br />
acts as an anode.<br />
It is well known that any periodic slow wave structure of N periods, when shorted<br />
appropriately at both ends, will exhibit (N+1) discrete resonant frequencies with phase<br />
shifts per period equally spaced between 0 and π. Generally speaking, these specific<br />
resonant modes can be determined experimentally and then used to fit a curve to give the<br />
complete dispersion function. Using the method described in Refs. [111, 112], the<br />
minima in the reflection trace present the resonance frequencies of the finite periodic<br />
waveguide, and satisfy the resonance condition<br />
φs = βsL=sπ, s=1,2 ... 24 (2.2)<br />
where φs is the phase shift, βs is the discrete wavenumber, and L is the waveguide length.<br />
The dispersion curve is constructed by the measured frequencies of the reflection minima<br />
and the discrete wavenumbers.<br />
The cavity resonances were measured with the reflection coefficient of the slow wave<br />
structure over the appropriate frequency range. The measured results at the first and<br />
second passbands are presented in Fig. 2.12 and Fig. 2.13, respectively. The curves show<br />
the measured resonant absorption peaks corresponding to 23 axial modes of the cavity.<br />
This was achieved by a scalar network analyzer (HP 8757A). The testing system setup is<br />
shown in Fig. 2.14. The waveguide dispersion (without electron beams) is shown as a<br />
Brillouin diagram in Fig. 2.15, as results from measurements of the waveguide reflection<br />
and transmission coefficients. The dots indicate the measurement points of the 2D<br />
periodic-waveguide. The dashed curve indicates the fundamental mode of the rectangular<br />
tube.<br />
36
(a)<br />
(b)<br />
(c)<br />
40 mm<br />
4×24 metal posts<br />
2×11.14 mm<br />
3×9.51 mm<br />
30 mm<br />
WR 187 choke flange<br />
φ 38 mm<br />
10 mm<br />
2 ¾ ″ flange<br />
welding<br />
20 mm<br />
600 mm<br />
Fig. 2.11. The periodic waveguide construction, (a) an overview,<br />
(b) a cross section view, and (c) a side view.<br />
37<br />
probes<br />
WR 187 waveguide<br />
WR 187<br />
choke flange
Fig. 2.12. The measured reflection curve at the first passband.<br />
Fig. 2.13. The measured reflection curve at the second passband.<br />
38
Frequency [GHz]<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
sweeper<br />
directional bridge<br />
Periodic waveguide<br />
Fig. 2.14. A block diagram of the testing system used for the<br />
measurement of the dispersion relation.<br />
-160 -80 0 80 160<br />
Wave number [1/m]<br />
Fig. 2.15. The measured Brillouin-diagram of the 2D periodic-waveguide (the dots<br />
indicate measurement points). The dashed curve indicates the fundamental<br />
mode of the rectangular tube.<br />
39<br />
HP 8757 A<br />
scalar network analyzer<br />
attenuator
2.1.5. Vacuum System Considerations<br />
In general, metals, ceramics, and some plastics, such as Teflon are satisfactory in<br />
systems having ultimate vacuums down to 5×10 -7 Torr. In this experiment, the main<br />
vacuum chamber is the periodic waveguide shown in Fig. 2.11. It connects with pump<br />
system through a 2 3 /4″ flange. The parts of feedthroughs and window are connected by<br />
O-ring type connectors. Generally, the tube is pumped down to a pressure less than 10 -6<br />
Torr by a Varian 20/l triode pump (model 911-5030). A Varian Turbo-V250 pump<br />
(model 969-9008) is used for rough pumping. Most of the time, the system will need to<br />
be baked to 100 0 C (since we have O-ring, this temperature can not be too higher).<br />
2.1.6. RF Diagnostics<br />
The details of the experimental diagnostic setup are shown in Fig. 2.16. The RF<br />
diagnostics can be classified into two aspects, power measurement and frequency<br />
diagnostic. For power measurements, a Schottky barrier diode is used to rectify and<br />
detect the envelope of a RF pulse, generating a nonlinear DC output in the instantaneous<br />
electric field. Then this DC output is recorded by a digital oscilloscope (Tektronix TDS<br />
540). A key factor to protect the detectors is the accurate attenuation of RF signals. Two<br />
methods of the frequency diagnostic are used, one based on the measurement by<br />
bandpass filters and the other based on the measurement by a frequency and time-interval<br />
analyzer (HP 5372A). A waveguide (WR 187) which has a cutoff frequency of 3.28 GHz<br />
is used. Afterward, two filters are used for a coarse survey of the frequency. Their<br />
bandpass are 5.68-7.45 GHz and 8.13-10.00 GHz, respectively. According to the coarse<br />
measurement of the frequency, a local signal (LO) from a synthesizer (HP 83752A) is<br />
selected. The LO signal is mixed with the RF output signal. Then the heterodyne IF<br />
signal is sent to the frequency and time-interval analyzer (HP 5372A) for the accurate<br />
frequency measurement. A power limiter is used to protect the frequency and timeinterval<br />
analyzer. All data are recorded and processed on-line with the aid of a PC. The<br />
communications are through GPIB interface cables and a HP VEE 3.0 software is used to<br />
collect data.<br />
40
cyclotron oscillator<br />
WR 187 waveguide<br />
DC block<br />
computer<br />
GPIB interface cable<br />
attenuator<br />
Tektronix TDS 540 oscilloscope<br />
RF out<br />
RF detector 1<br />
bandpass<br />
filter<br />
divider<br />
divider<br />
HP 5372A frequency and<br />
time-interval analyzer<br />
Fig. 2.16. The experimental diagnostic setup. It includes power<br />
measurement and frequency diagnostic.<br />
41<br />
power limiter<br />
RF detector2<br />
GPIB interface cable<br />
HP 5364A microwave<br />
mixer/detector<br />
RF<br />
IF<br />
L.O.<br />
HP 83752A<br />
synthesized sweeper
2.2. Experimental Operation<br />
Each experiment began with a warm-up period, typically a few hours, to activate the<br />
cathodes. Initially, the filaments were operated at a potential, of ~6 V. Then the potential<br />
was gradually increased to ~8 V in order to obtain the desired currents. For used<br />
cathodes, this potential has to be increased to 11 V. In the two-beam CRM experiment,<br />
we used two individual AC power supplies to heat the cathodes separately in order to get<br />
a uniform current in each beam. The AC supplies must isolate the electron gun voltage<br />
from the ground potential. The electron gun was adjusted to provide a 0.2 ms pulse at the<br />
desired current level (0.1-0.5 A). Typical voltage pulse of the electron gun and the beam<br />
current trace are illustrated in Fig. 2.17. The beam current was measured by a<br />
10Ω resistor placed between collector and ground. In the experiment, the periodic<br />
waveguide is connected to a ground potential, and the collector has to be isolated from<br />
the ground.<br />
The adjustment of the solenoid position, the calibrations of the diagnostic system, and<br />
cold measurements were conducted prior to each experiment. The desired uniform axial<br />
magnetic field was obtained by adjusting the solenoid position properly (the current trace<br />
in the collector should be clear), and by adjusting the peak level of the current pulse in<br />
the solenoid. Any directional change of the electron beams requires the re-alignment of<br />
the solenoid.<br />
The experiment was initiated by the main pulser, solenoid pulser; sequentially<br />
following by the kicker current pulser, the electron gun voltage pulser, and the data<br />
acquisition system. Except the RF signal diagnostic, the results to be recorded include the<br />
collector current, the solenoid current pulse, the kicker current pulse, and the electrongun<br />
voltage pulse during the experiment. When we seek the RF signal, we scanned the<br />
axial magnetic field in the design region, accompanied by a scan of the kicker current.<br />
The electron energy distribution was determined with the timing relationship between the<br />
electron gun pulse, axial magnetic field and kicker current. Attenuators were used at each<br />
experiment in order to protect the detectors.<br />
42
E-gun Voltage [kV]<br />
Current [A]<br />
15<br />
10<br />
5<br />
0<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
(a)<br />
-20 0 20 40 60 80 100 120 140 160<br />
Time [us]<br />
(b)<br />
-20 0 20 40 60 80 100 120 140 160<br />
Time [us]<br />
Fig. 2.17. An electron gun voltage trace (a) and a single beam current trace (b).<br />
43
2.3. Experimental Results<br />
The 2D CRM-array experiment has been operated with one and two electron beams,<br />
as illustrated in Fig. 1.5b by dashed and solid curves, respectively. A single electronbeam<br />
in the center channel yielded the results shown in Figs. 2.18 and 2.19. The detector<br />
output trace is presented in Fig. 2.18a, together with the electron-beam energy trace. The<br />
frequency characteristic of the RF output signal is shown in Fig. 2.18b as measured<br />
during the pulse (the dots present the points of the measurement). The axial magnetic<br />
field in this run is 2.9 kG, which corresponds to a cyclotron frequency of 8.0 GHz. The<br />
current measured in the collector is ~0.1A. The average radiation frequency is 7.5 GHz,<br />
hence the device operates with a backward wave. This effect is clearly observed in Figs.<br />
2.18a,b by the curvatures of the voltage and frequency traces (note that in a backward<br />
wave interaction, the frequency decreases as the electron energy increases). A slightly<br />
higher electron energy results in a rabbit-ears shape of the detector output, as shown in<br />
Fig. 2.19. The optimal resonance in this tuning condition is satisfied below the maximum<br />
voltage.<br />
Single-beam measurements have been made in a wide range of axial magnetic fields<br />
and electron gun voltages. Oscillations were observed in different frequencies as shown<br />
in Figs. 2.20a-d. In all cases, the RF frequency tends to decrease as the electron energy<br />
increases. For axial magnetic fields in the range 2.6-2.9 kG (Figs. 2.20a-c), the<br />
corresponding wave frequency varies within 6.87-7.52 GHz, respectively, in the first<br />
passband of the periodic waveguide. For an axial magnetic field of 3.7 kG, interactions<br />
were observed in the second passband (9.75 GHz), as shown in Fig. 2.20d. In the second<br />
passband, the coupling is much smaller since the interaction occurs mostly with the<br />
second transverse mode, which has a null in the center. The emission in this case may<br />
result from the finite width of the electron beam, or from its slightly off-axis propagation.<br />
The CRM-array was operated also with a single electron-beam in the side channel. A<br />
typical result for a 2.7 kG magnetic field is presented in Fig. 2.21. The extracted power of<br />
the RF sample by the various couplers in all the single beam measurements was in the<br />
range of 5-25 W. This power level is sufficient for spectral measurements.<br />
44
Frequency [MHz]<br />
Detector output [mv]<br />
45<br />
30<br />
15<br />
0<br />
7,540<br />
7,520<br />
7,500<br />
7,480<br />
(a)<br />
60 90 120<br />
0<br />
150<br />
Time [us]<br />
(b)<br />
60 90 120 150<br />
Time [us]<br />
Fig. 2.18. Experimental results of the one-beam CRM oscillator at 2.9 kG:<br />
(a) the electron gun voltage (upper curve) and the detector RF<br />
output (lower curve), (b) the frequency variation during the pulse.<br />
45<br />
9<br />
6<br />
3<br />
E gun voltage [kV]
Detector output [mv]<br />
Frequency [MHz]<br />
45<br />
30<br />
15<br />
0<br />
6,930<br />
6,900<br />
6,870<br />
6,840<br />
(a)<br />
40 80 120 160<br />
Time [us]<br />
(b)<br />
40 80 120 160<br />
Time [us]<br />
Fig. 2.19. An off-tuned operation at 2.7 kG: (a) the electron gun voltage<br />
(upper curve) and the detector RF output (lower curve), (b) the<br />
frequency variation during the pulse.<br />
46<br />
9<br />
6<br />
3<br />
0<br />
E gun voltage<br />
[kV]
Frequency [MHz]<br />
Frequency [MHz]<br />
6,890<br />
6,885<br />
6,880<br />
6,875<br />
7,100<br />
7,095<br />
7,090<br />
7,085<br />
(a)<br />
5.5 6.5 7.5 8.5<br />
Electron energy [keV]<br />
(b)<br />
5.5 5.7 5.9 6.1 6.3 6.5<br />
Electron energy [keV]<br />
Fig. 2.20. Tuning characteristics of a one-beam CRM, at (a) 2.6 kG, (b) 2.7 kG.<br />
47
Frequency [MHz]<br />
Frequency [MHz]<br />
7,525<br />
7,520<br />
7,515<br />
7,510<br />
9,754<br />
9,753<br />
9,752<br />
(c)<br />
5.5 6.0 6.5 7.0 7.5<br />
Electron energy [keV]<br />
(d)<br />
3.0 3.5 4.0 4.5<br />
Electron energy [keV]<br />
Fig. 2.20. (Cont.) Tuning characteristics of a one-beam CRM, at (c) 2.9 kG, (d) 3.7 kG.<br />
48
Detector output [mv]<br />
Frequency [MHz]<br />
450<br />
300<br />
150<br />
0<br />
6,930<br />
6,900<br />
6,870<br />
6,840<br />
(a)<br />
0 25 50 75<br />
Time [us]<br />
(b)<br />
0 25 50 75<br />
Time [us]<br />
Fig. 2.21. A 2D CRM-array operation with a single beam in an off-axis side<br />
channel at 2.7 kG: (a) the electron gun voltage (upper curve) and<br />
the detector RF output (lower curve), (b) the frequency variation<br />
during the pulse.<br />
49<br />
9<br />
6<br />
3<br />
0<br />
E gun voltage [kV]
The 2D CRM-array was operated with two electron beams as shown in Fig. 1.5b.<br />
Typical curves of the detector output and the electron gun voltage pulse are shown in Fig.<br />
2.22a. A frequency variation of the RF output signal is shown in Fig. 2.22b. The axial<br />
magnetic field in this run is 2.7 kG, which corresponds to a cyclotron frequency of 7.56<br />
GHz. The average radiation frequency is 6.9 GHz, hence the device operates again in the<br />
backward-wave regime. In a CRM operation with an electron-energy slightly higher than<br />
the optimal value, the synchronism condition takes place in the leading and trailing edges<br />
of the voltage pulse, as shown in Fig. 2.23.<br />
By increasing the axial magnetic field, the two-beam CRM oscillates also at 3.8 kG.<br />
Figs. 2.24a,b show the electron gun voltage, the detector output and the intra-pulse<br />
frequency variation in this case. The corresponding cyclotron frequency is 10.64 GHz<br />
and the radiation frequency is 6.7 GHz. This result was obtained without a kicker field.<br />
Comparing to the one-beam CRM experiments, in the two-beam CRM experiment, the<br />
cathodes have off-axis positions. Then the transverse magnetic field exists for both<br />
cathodes. The transverse velocity of the electrons for the CRM interaction in this case<br />
may result from the nature kicking of the solenoid magnetic field.<br />
A series of measurements were made in different electron gun voltages in axial<br />
magnetic fields of 2.7 kG and 3.8 kG (7.56 GHz and 10.64 GHz cyclotron frequencies,<br />
respectively). For 2.7 kG, the corresponding wave frequency is around 6.9 GHz, and the<br />
sampled output power by the probe is ~20 W. For an axial magnetic field of 3.8 kG, the<br />
interaction occurs around 6.7 GHz without a kicker, and the sampled output power is<br />
~6 W. Maps of RF-frequency vs. electron-energy accumulated in many runs are shown in<br />
Figs. 2.25a and b for 2.7 kG and 3.8 kG, respectively (note that each dot presents average<br />
values of the corresponding run). The electron energy acceptance for 2.7 kG is much<br />
larger than for 3.8 kG, presumably because of the smaller Doppler shift.<br />
50
Frequency [MHz]<br />
Detector output [mv]<br />
90<br />
60<br />
30<br />
0<br />
6,865<br />
6,860<br />
6,855<br />
6,850<br />
(a)<br />
55 60 65 70<br />
Time [us]<br />
(b)<br />
55 60 65 70<br />
Time [us]<br />
Fig. 2.22. A two-beam CRM oscillator output at 2.7 kG: (a) the detector<br />
output (sharp curve) and the electron gun voltage (flat curve),<br />
(b) the frequency variation during the pulse.<br />
51<br />
9<br />
6<br />
3<br />
0<br />
E gun voltage [kV]
Detector output [mv]<br />
Frequency [MHz]<br />
450<br />
300<br />
150<br />
0<br />
6,910<br />
6,880<br />
6,850<br />
6,820<br />
(a)<br />
0 30 60 90<br />
Time [us]<br />
(b)<br />
0 30 60 90<br />
Time [us]<br />
Fig. 2.23. An off-tuned operation of two-beam CRM oscillator: (a) the<br />
electron gun voltage (upper curve) and the detector output<br />
(lower curve), (b) the frequency variation during the pulse.<br />
52<br />
9<br />
6<br />
3<br />
0<br />
E gun voltage [kV]
Detector output [mv]<br />
Frequency [MHz]<br />
180<br />
120<br />
60<br />
0<br />
6,900<br />
6,800<br />
6,700<br />
6,600<br />
(a)<br />
20 50 80 110<br />
Time [us]<br />
(b)<br />
20 50 80 110<br />
Time [us]<br />
Fig. 2.24. A two-beam CRM operation at high magnetic field, 3.8 kG:<br />
(a) the electron gun voltage (upper curve) and the detected<br />
RF output (lower curve), (b) the frequency variation.<br />
53<br />
12<br />
8<br />
4<br />
0<br />
E gun voltage [kV]
Frequency [MHz]<br />
Frequency [MHz]<br />
7,500<br />
7,000<br />
6,500<br />
6,000<br />
7,500<br />
7,000<br />
6,500<br />
6,000<br />
(a)<br />
0 4 8 12<br />
Electron energy [keV]<br />
(b)<br />
54<br />
B0=2.7 kG<br />
B0=3.8 kG<br />
0 4 8 12<br />
Electron energy [keV]<br />
Fig. 2.25. Maps of frequency vs. electron-energy accumulated in many runs<br />
around (a) 2.7 kG and (b) 3.8 kG magnetic fields (each dot<br />
represents the average of a single run).
2.4. Analysis and Discussions<br />
For the one-beam 2D CRM-array experiment, the agreement between the<br />
experimental results (Figs. 2.20a-d) and the theoretical tuning relation (Eq. 1.1 and Fig.<br />
2.15) can be evaluated by a mismatch parameter proposed as follows<br />
2<br />
⎡ β 0 ( ω)<br />
v0<br />
⎤<br />
∆ = ⎢ ⎥ −1<br />
. (2.3)<br />
⎣ ω c − ω ⎦<br />
This parameter is computed using the measured experimental data (i.e., the<br />
wavenumber ( )<br />
β 0 ω , the total electron velocity 0<br />
55<br />
v , and the cyclotron frequency ω c are<br />
computed by the instantaneous em frequency, electron gun voltage and solenoid current,<br />
respectively). Eq. 1.1 and Eq. 2.3 teach that<br />
2<br />
( z ) v v ∆ ≅ ⊥ , where ⊥<br />
v is the initial electron<br />
transverse velocity. Hence, the expected value for ∆ is in the order of one due to the<br />
actual v ⊥ induced by the kicker (note that v ⊥ is not measured in this experiment). Fig.<br />
2.26 shows the results of ∆ computed by Eq. 2.3 for the experimental runs presented in<br />
Figs. 2.20a-d, respectively. Negative values of ∆ in Fig. 2.26 can be attributed to the<br />
error range of the solenoid field measurement (~2 %), and to the high sensitivity of Eq.<br />
2.3 to the cyclotron frequency (note that ω ~ ω ). Nevertheless, a result of<br />
− 07 . < ∆ < 19 . indicates a reasonable agreement between experiment and theory.<br />
Delta<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
-0.5<br />
-1<br />
(d)<br />
(b)<br />
3 4 5 6 7 8 9<br />
Electron energy [keV]<br />
Fig. 2.26. The mismatch parameter ∆ (Eq. 2.3). The curves denoted a-d<br />
correspond to the results in Figs. 2.20a-d, respectively.<br />
c<br />
(c)<br />
(a)
The theoretical tuning condition of the CRM interaction (Eq. 1.1) and the Brillouin<br />
dispersion diagram of Fig. 2.15 are applied to analyze possible mechanisms for the<br />
resonant microwave radiation observed in the one- and two-beam 2D CRM-array<br />
experiments. The CRM tuning conditions observed in the one-beam 2D CRM-array<br />
experiment are illustrated in Fig. 2.27. The Brillouin diagram based on measurements<br />
shows the periodic-waveguide dispersion in the first and second passbands. The electronbeam<br />
lines are computed by Eq. 1.1 according to the experimental parameters for<br />
B 0 = 2.7 kG and 3.8 kG. The intersection points between the electron-beam lines and the<br />
waveguide dispersion curves indicate the em resonance frequencies. The results for the<br />
backward-wave interaction agree with the experimental results.<br />
The synchronism conditions observed in the two-beam 2D CRM-array experiment<br />
are illustrated in Fig. 2.28. Again, the Brillouin diagram (based on measurements) shows<br />
the periodic-waveguide dispersion. The electron-beam lines are computed by Eq. 1.1 for<br />
2.7 kG and 3.8 kG, and for electron energies of 6.5 keV and 10.2 keV, respectively. The<br />
intersection points between the electron-beam lines and the waveguide dispersion curves<br />
indicate the CRM resonance frequencies. One intersection point (at 2.7 kG) is in the fastwave<br />
region, whereas the other (at 3.8 kG) is in the slow-wave region. Both interactions<br />
occur with backward waves. In the first 2D CRM experiment with the two electrom<br />
beams, the CRM tuning results indicate clearly interactions with backward waves, and<br />
with fast and slow spatial harmonics of the periodic structure. The two-beam CRM<br />
interactions occur near the cutoff frequency of the first passband. The tuning condition<br />
for the fundamental harmonic interaction leads to a wide electron energy acceptance, as<br />
observed in this experiment (note the ~6 keV spread in Fig. 2.25a).<br />
These experiments provide some information on the multi-beam CRM spectral<br />
character. However, the multi-beam CRMs, which consisted of multi-beam electron<br />
guns, resonator systems, focusing magnets and collectors, are highly sophisticated<br />
systems due to the non-uniformity of the RF distribution in the cavity and the transverse<br />
contribution of the focusing magnetic field. One of the most difficult tasks is to develop<br />
an electron gun, which produces the multi-beam streams.<br />
56
Frequency [GHz]<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
d<br />
b<br />
2<br />
-160 -80 0 80 160<br />
c<br />
a<br />
Wave number [1/m]<br />
Fig. 2.27. The one-beam CRM tuning diagram. The upper two curves show the periodic-waveguide<br />
dispersion in the first and second passbands. The lines present the electron-beam lines as the<br />
results from Eq. 1.1. The dashed curve indicates the fundamental mode of the rectangular tube.<br />
Slow<br />
Frequency<br />
[GHz]<br />
10.6<br />
10.2 keV<br />
9 6.5 keV<br />
Fast<br />
12<br />
7.5<br />
6<br />
-500 -300 -100 100 300 500<br />
Wave number [ 1/m]<br />
Fig. 2.28. A tuning-diagram presentation of Eq. 1.1 with the waveguide dispersion (Fig. 2.15), for the<br />
results of the two-beam CRM-array. The electron-beam lines, for 6.5 keV / 2.7 kG and 10.2<br />
keV / 3.8 kG, show CRM interactions with fast and slow backward waves, respectively.<br />
57<br />
3.8 kG<br />
2.7 kG
At present, we use the 2D simulation code, EGUN, commonly used in vacuum<br />
electronics, to design the multi-beam electron gun. However, these simulations do not<br />
obtain complete convergent results in the real systems, which lack 2D symmetry<br />
structures. The structure in the multi-beam electron gun is not the optimal focusing<br />
electrode, which arranges the uniform distribution of the current density in the multibeam<br />
device. Some improvement in the design of the multi-beam electron gun is<br />
necessary in the future since it will affect average power. To achieve this goal, it is<br />
necessary to use advanced 3D modeling codes to design the components in multi-beam<br />
CRM devices.<br />
2.5. Conclusions<br />
The spectral measurements show clearly the CRM interaction with backward spatial<br />
harmonics. Both, fast- and slow-wave CRM interactions are observed in the two-beam<br />
CRM experiment. The results of the two-beam CRM experiment show the feasibility of<br />
splitting the electron current to separate beams in the array. The same approach leads to<br />
the construction of advanced CRM-array experiments in our laboratory (2D and 3D<br />
arrays of five (carbon-fiber) and nine (thermionic) cathodes, respectively). The next<br />
challenge is probably to improve the RF output power of the multi-beam CRM devices.<br />
The complexity of the multi-beam design requires the development of advanced software<br />
and equipment, such as power supplies. However, those problems can be remedied.<br />
Specially, when 3D modeling codes become mature, they certainly will accelerate the<br />
development of the devices that lack 2D symmetry and alleviate the design difficulties<br />
for multi-beam CRMs. The optimism in multi-beam CRMs is based on current<br />
developments on 3D modeling codes and the spectral measurements in this work.<br />
Further studies proposed for the development of the multi-beam CRM-array concept<br />
[60] include (a) a radiation power extraction and efficiency measurements, (b) an<br />
investigation of coupling effects between several electron beams in a 2D array, (c)<br />
development of large 3D CRM-arrays, (d) studies of direct radiation from CRM arrays,<br />
and (e) active phased-array antenna features and radiation steering.<br />
58
Chapter 3<br />
The Carbon-Fiber CRM-Array Experiment<br />
This chapter presents the first experimental study of a carbon-fiber CRM-array. The<br />
CRM-array is operated here with the multi-beam cold-cathode array, made of a carbonfiber<br />
cathode array. According to our knowledge this is the first exploration of the multibeam<br />
cold-cathode array and its application in vacuum electronics.<br />
The next section, Section 3.1, describes the experimental design and setup of the<br />
carbon-fiber CRM-array. It includes the mechanical design of the device, a study of the<br />
multi-beam carbon-fiber cathode array, the design of the periodic waveguide and magnetic<br />
fields. In this part, the study of the multi-beam carbon-fiber cathode array is described<br />
intensively in the subsection 3.1.2. The fabrication of the carbon-fiber cathode is described<br />
first. Then, the experimental design and setup of the multi-beam carbon-fiber cathode<br />
array is presented. It includes the design of an electron-optic system of the multi-beam<br />
electron gun, a multi-channel pulsed power device, and an accelerating DC high voltage<br />
supply. The experimental results from the large area field emission “arrays” are given, and<br />
the general nature of voltage and current traces is presented. The effect of beam<br />
multiplication is discussed.<br />
The operation of the carbon-fiber CRM experiment is described in Section 3.2. The<br />
experimental results and discussions are presented in Sections 3.3 and 3.4, respectively.<br />
3.1. Experimental Design and Setup<br />
A photograph of the carbon-fiber CRM-array experimental device is shown in Fig.<br />
3.1. The oscillator tube consists of the electron gun with multi-beam carbon-fiber cathode<br />
array, a 2D periodic waveguide, a collector, a solenoid, and a kicker coil, which imparts<br />
initial transverse velocity to the electrons. The total length of the device is about 1.2<br />
meter.<br />
59
Fig. 3.1. Photograph of the carbon-fiber CRM-array experimental setup.<br />
60
A schematic diagram of the carbon-fiber CRM-array experiment is shown in Fig. 3.2.<br />
The electron beams are emitted from the multi-beam carbon-fiber cathode array, which is<br />
driven by a multi-beam electron gun pulser. Then, the multiple electron beams, in<br />
energies of less than 10 keV, are spun up by the kicker, injected into the corresponding<br />
channels in the 2D periodic waveguide, and interact with the em wave. The ignition of<br />
each cathode causes an abrupt fall in its voltage, down to around 1 kV during emission.<br />
The solenoid field is compensated by Helmholtz coils and five blaster resistors act as<br />
current limiters. The accelerating voltage between the grid and the anode is provided by<br />
the DC high-voltage source. The beam currents are monitored by Rogowsky coils. The<br />
periodic waveguide is terminated by half-period reflecting sections at both ends.<br />
The output signal is radiated from the exit plane of the waveguide to free-space, and is<br />
detected in the near-field by a horn antenna. The signal is attenuated and divided into two<br />
arms. In one arm, the signal is detected by a crystal detector (HP 424A) and recorded by a<br />
digital oscilloscope (Tektronix TDS 540). In the other arm, the signal passes a 4.7-<br />
5.3GHz bandpass filter (B.P.F.) in order to identify the frequency range of the RF signal.<br />
All data are collected by a computer using a HP VEE 3.0 (or Tektronix Wavestar)<br />
software. The experimental parameters are listed in Table 3.1.<br />
Although the carbon-fiber cathode can work at pressure above 10 -6 Torr, a better<br />
vacuum improves its operation. In this experiment, the tube is pumped down to a pressure<br />
around 10 -6 Torr.<br />
3.1.1. Mechanical Design<br />
An overview of the apparatus of the carbon-fiber CRM-array experiment is shown in<br />
Fig. 3.3. A 1.4 m high frame is used to assemble the apparatus in vertical orientation. The<br />
main vacuum chamber consists of a stainless steel vessel and a glass tube. The vessel has<br />
a 6 inch diameter, one 4 inch hole at the top and two 4 inch flanges on the side. The side<br />
sections are attached to a Varian 20 litre/s triode pump (model 911-5030) and a Varian<br />
Turbo-V250 pump. The top hole is attached to the glass tube, which has 10 cm diameter<br />
and 1 m length. An O-ring is used between the two parts in order to protect the vacuum.<br />
61
laster resistors<br />
multi-beam<br />
electron gun<br />
pulser<br />
carbon-fiber<br />
cathodes<br />
kicker<br />
grid<br />
anode<br />
periodic<br />
waveguide<br />
oscilloscope<br />
Fig. 3.2. Schematic of the carbon-fiber CRM-array experiment.<br />
Table 3.1. Experimental parameters.<br />
Electron beams:<br />
energy ~5 keV<br />
current per beam ~ 0.1 A<br />
pulse duration 0.4 ms<br />
number of beams<br />
Magnetic field:<br />
3 or 5<br />
solenoid ~2.4 kG<br />
kicker ~ 0.7 kA turns<br />
Periodic waveguide:<br />
rectangular tube 69 × 22 mm 2<br />
length 64 cm<br />
post diameter 2 mm<br />
post array 6× 20<br />
transverse periodicity 11.5 mm<br />
axial periodicity 30 mm<br />
62<br />
DC high<br />
voltage<br />
vacuum<br />
glass tube<br />
detector<br />
detector<br />
solenoid<br />
collector<br />
H.P.F<br />
attenuator<br />
splitter<br />
B.P.F<br />
antenna
vacuum<br />
glass tube<br />
solenoid<br />
periodic<br />
waveguide<br />
anode<br />
grid<br />
kicker<br />
carbon-fiber<br />
cathodes<br />
10 mm<br />
8 mm<br />
φ 100 mm<br />
Fig. 3.3. Apparatus of the carbon-fiber CRM-array experiment.<br />
63<br />
collector<br />
10.8 mm<br />
50 mm 120 mm<br />
50 mm<br />
630 mm<br />
220 mm<br />
4 inch flange<br />
6 inch flange<br />
Magnetic components<br />
Bronze copper<br />
Copper<br />
Stainless steel<br />
Glass<br />
Tungsten<br />
Ceramic<br />
O-ring
The periodic waveguide is assembled inside the glass. A horn antenna outside the glass is<br />
coupled to the interaction region inside (note that unless the glass is λ/2 thick, or its<br />
mismatch can be matched at both surfaces, the near field antenna may distort the radiation<br />
pattern or lead to frequency sensitivity due to multiple internal reflections [113]). The stalk,<br />
supported the electron gun and the periodic waveguide, has a length of about 28 cm. It<br />
consists of several stainless steel posts and disks. Ceramic pieces are used for insulation.<br />
Eight Tungsten feedthroughs are hermetically sealed into the glass. The high voltages are<br />
connected through these feedthroughs. High voltage probes, Rogowsky coils, and pulsed<br />
power supplies are installed in an adjacent rack mount.<br />
3.1.2. Multi-beam Carbon-fiber Cathode Arrays<br />
Explosive electron emission cathodes for microwave applications offer the potential to<br />
provide high efficiency electron guns due to larger current densities and direct<br />
modulations of emitted beams. This research is motivated by the desire to develop<br />
efficient, reliable and cost-effective multi-beam cathode arrays for multi-beam vacuum<br />
electronic devices, such as multi-beam CRM-arrays and low voltage, long wavelength<br />
multi-beam FEL arrays. The primary objective for this stage is to make an effective fivebeam<br />
carbon-fiber cathode array and explore the operation of multi-beam cold-cathode<br />
arrays in vacuum electronic devices.<br />
3.1.2.1. Experimental Configuration<br />
A schematic diagram of the multi-beam carbon-fiber cathode array experimental setup<br />
is shown in Fig. 3.4. The system consists of a multi-beam electron gun and a solenoid.<br />
The gun consists of two gaps. One gap is from five cathodes to a grid. This gap provides<br />
the electric field for the cathodes’ emission. The other gap is from the grid to an anode.<br />
This gap provides an acceleration of the electrons in order to increase the energy of the<br />
electrons for CRM interaction. The construction of the first section is similar to the<br />
electron gun construction described in Section 2.1.1. The accelerating gap, which avoids<br />
the need for a high electric field in the first section, and delays the breakdown of the<br />
system, is powered with a DC high voltage supply. The five cathodes are made of<br />
bundles of carbon fibers. Each bundle contains hundreds of fibers in a copper pipe (~2<br />
64
mm inner diameter). The diameter of each carbon fiber is less than 10 µm. The distance<br />
between two adjacent cathodes is 11.5 mm. The electrodes are placed inside a glass tube<br />
and are connected to the multi-channel electron gun pulser through the glass tube. The<br />
grid is located 8 mm ahead of the cathodes, and the distance between the grid and the<br />
anode is 10 mm. Both the grid and the anode are connected to Tungsten feedthroughs,<br />
which are hermetically sealed into the glass. The grid is connected to a ground potential<br />
outside and the anode is connected to a DC high voltage supply, which can provide up to<br />
20 kV DC voltage.<br />
The electron beams are emitted from the carbon-fiber cathodes, propagate in the two<br />
sections, and are collected by a metal plate. The collected current is measured by means of<br />
a 10 Ω resistor. The device is activated by a multi-channel electron gun pulser, a high<br />
voltage DC power supply, and a solenoid pulser. A Rogowsky coil (1:10 V/A) is used to<br />
monitor the output current from the electron gun pulser. Five blaster resistors, ~10 kΩ<br />
CuSO4 water resistors, are connected to the five cathodes in series separately and act as<br />
current limiters. High resistivity enables more tips to emit, and the magnitude of the<br />
emission from each cathode is more uniform. The emitter voltage, which is the potential<br />
between the cathodes and the grid, and the DC high voltage are monitored by two high<br />
voltage probes (Tektronix P6015A, 1:1000). All data are recorded by several digital<br />
oscilloscopes (Tektronix TDS 210), and collected in a computer by a Tektronix Wavestar<br />
software through GPIB cables. All cathodes testing are carried out with a base pressure<br />
around 10 -6 Torr, with and without an external magnetic field.<br />
high voltage<br />
probe<br />
multi-beam<br />
electron<br />
gun pulser<br />
blaster resistors<br />
carbon-fiber<br />
cathodes<br />
grid<br />
anode<br />
Fig. 3.4. Schematic of the multi-beam carbon-fiber cathode array experiment.<br />
65<br />
DC high voltage<br />
solenoid<br />
10 Ω<br />
collector<br />
vacuum<br />
glass tube<br />
oscilloscope
3.1.2.2. Cathode Fabrications<br />
The schematic of the carbon-fiber cathode is shown in Fig. 3.5. In Fig. 3.5a, the<br />
cathode consists of 10 µm bunches of fibers and a copper tube. During fabrication, a<br />
bundle of carbon fibers, contained hundreds of fibers, was trimmed (but not etched) and<br />
inserted by hands in the copper tube. The tube was mechanically pressed at the end in<br />
order to tighten the fiber bundle and to provide a proper electrical contact. An advanced<br />
scheme is shown in Fig. 3.5b. Comparing to the scheme in Fig. 3.5a, the cathode adds an<br />
electrical field shield around the tips of the carbon fibers. It improves the electrical field<br />
distribution for the cathodes’ emission. When a voltage is applied to the tube, the electric<br />
field created at the tips is magnified due to the extreme sharpness of the tips, which causes<br />
electron emissions. In many cases an electric field as low as 3 kV/cm is sufficient to<br />
produce plasma formation for electron emissions. A photograph of the cathodes is shown<br />
in Fig. 3.6.<br />
2 mm<br />
3 mm 3 mm<br />
(a) (b)<br />
Fig. 3.5. Schematic of a bunched carbon-fiber cathode (a) and<br />
an advanced scheme (b).<br />
Fig. 3.6. Examples of the end brush cathodes.<br />
66<br />
2 mm
3.1.2.3. Electron Trajectories<br />
The electron optics design of the multi-beam electron gun is performed with the<br />
EGUN code with a few assumptions. As in Section 2.1.1, we assumed that each beam has<br />
a perfect local symmetry around its own axis and the gap between cathode and grid (or<br />
grid and anode) is much smaller than the distance between two holes of the grid plate (or<br />
the anode plate). So simulating the center electron flow and simplifying the boundary, the<br />
code output for a 3mm carbon-fiber cathode with 8 mm cathode-grid gap and 10 mm<br />
accelerating section is shown in Fig. 3.7. Fig. 3.7a shows electron gun geometry and beam<br />
trajectory. It includes three regions: a cathode-grid region, a grid-anode region, and a<br />
beam tunnel. Fig. 3.7b and Fig. 3.7c present electron density versus radius and the angle<br />
of the electron motion measured from the z-axis, respectively. A magnetic field is used for<br />
the beam focusing.<br />
R (mm)<br />
Fig. 3.7. The EGUN code output for a 3mm carbon-fiber cathode,<br />
(a) the beam trajectory (radius (R) vs. axial length (Z)).<br />
67<br />
Z<br />
( mm)
Current density (0.119 A/mm 2 )<br />
Fig. 3.7. (Cont.) The EGUN code output for a 3mm carbon-fiber cathode, (b) electron density vs.<br />
radius, (c) the angle of the electron motion measured from the z axis.<br />
68<br />
R<br />
( mm)<br />
R ( mm)
3.1.2.4. Power Supplies<br />
Three incorporating high voltage supplies for the multi-beam electron gun,<br />
accelerating section, and solenoid were used in the experiment of the carbon-fiber cathode<br />
array. The solenoid pulser is the same as described in Section 2.1.3. However, the multi<br />
channel electron gun pulser was redesigned in order to ensure the uniform current density<br />
of the multi-cathode array. Meanwhile, the DC high voltage was used for the accelerating<br />
gap. The design details are described in the section below.<br />
The multi-channel pulsed power system produces five separating pulses with fairly<br />
high voltages and output currents. The circuit is shown in Appendix B3. The pulser is fed<br />
by 220 V AC through a variable voltage transformer and a 10 A fuse. Then, this AC<br />
voltage is connected to a 220/460 V up-shift transformer. The output of the transformer is<br />
fed to five-channel charging circuits. Each channel consists of a low-voltage capacitor<br />
bank (C), a diode IN5408 that prevents a reverse recharging of the capacitor, and a<br />
transformer (car ignition coil). The charging voltage is monitored by a TY-43 digital panel<br />
meter. An SCR control circuit is used as a common gate. The five capacitors, about 10uF<br />
each, are charged with a rectified main voltage (600V), and then are discharged in an<br />
instant through the SCR and the ignition coils. The SCR is triggered by a function<br />
generator.<br />
The DC high voltage supply for the acceleration section was done in two schemes.<br />
Both of them used a modified Model 615 Pulserad power supply. The original Model 615<br />
Pulserad and our modifications are described in Appendix C. The circuits for both<br />
schemes are shown in Fig. 3.8 and Fig. 3.9, respectively. In Scheme 1, a long pulse is<br />
used to supply the accelerating stage. Compared to the electron gun voltage pulse, the<br />
duration of the pulse is much longer and it acts as a DC high voltage. A timing diagram in<br />
scheme 1 is shown in Fig. 3.10. In Scheme 2, the DC high voltage is coming directly from<br />
a charged capacitor bank in the modified Model 615 Pulserad. For safety, the capacitors<br />
are discharged after the shot of the electron gun. A corresponding timing diagram is<br />
shown in Fig. 3.11.<br />
69
CRM<br />
system<br />
1 kΩ<br />
1 kΩ<br />
Fig. 3.8. Circuit of a accelerating voltage source.<br />
Spark gap<br />
Spark gap<br />
50 kV pulse<br />
50 kV pulse<br />
20 kV<br />
1.5 kΩ<br />
1 µF<br />
20 kV<br />
1.5 kΩ<br />
1 µF<br />
Fig. 3.9. Circuit of a DC high voltage source.<br />
70<br />
PT-55<br />
Trigger amplifier<br />
High DC<br />
voltage supply<br />
PT-55<br />
Trigger amplifier<br />
High DC<br />
voltage supply<br />
Control<br />
function<br />
panel<br />
CRM<br />
system<br />
Control<br />
function<br />
panel
Emitter voltage [kV]<br />
Emitter voltage [kV]<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
5<br />
0<br />
-5<br />
-10<br />
0 100 200 300 400<br />
Time [us]<br />
Fig. 3.10. A timing diagram in Scheme 1.<br />
0 200 400 600 800<br />
Time [us]<br />
Fig. 3.11. A timing diagram in Scheme 2.<br />
71<br />
20<br />
15<br />
10<br />
5<br />
0<br />
20<br />
15<br />
10<br />
5<br />
Accelerating voltage [kV]<br />
Accelerating voltage [kV]
3.1.2.5. Electrical Performance<br />
The electron gun, which has one carbon-fiber cathode, was tested initially at a diode<br />
voltage of more than 4 kV (without accelerating voltage) with an 8 mm gap between the<br />
cathode and the grid. A ~100 mA diode current was observed. Then, increasing the<br />
number of the cathodes to three and five, the electron gun was tested in the same<br />
condition. Typical emitter voltage (or diode voltage) and current traces for a shot with the<br />
electron gun, which has five carbon-fiber cathodes, are illustrated in Fig. 3.12 (without an<br />
additional accelerating voltage). In this shot, the multi-channel gun pulser was adjusted to<br />
provide a more than 3 kV/cm electric field for each cathode. In Fig. 3.12, the emitter<br />
voltage rises rapidly (~2kV) during the first few microseconds. Then, the voltage drops<br />
sharply to ~500 V due to the impedance changing as the current turns on. After about<br />
450 µs there is a breakdown between the cathodes and the grid. This attributes to the<br />
property of explosive field-emission cathodes. Then the closure speed is about 1.8 cm/ms.<br />
The collector current was measured by a 10 Ω resistor placed between the collector and<br />
ground. A ~0.5 A current (total) was measured at the collector, that is about 0.1 A for<br />
each channel. The current density is around 1.4 A/cm 2 (7 A/cm 2 in the cathode-grid gap<br />
since we monitored the ~0.5 A input current for each cathode). Therefore, a long duration<br />
pulse dictates a low current density. The relative long rise time of the high voltage pulse<br />
caused the carbon fibers flare on a critical voltage. This may explain the long duration<br />
pulse with a low current density, relative to other one-beam cold-cathode researches.<br />
Adding an accelerating voltage, typical emitter voltage and current traces for a shot with<br />
five carbon-fiber cathodes are illustrated in Fig. 3.13. The pulse duration of the emitter<br />
voltage for a one channel is not significantly changed. So it seems that the accelerating<br />
voltage did not change the closure speed in the cathode-grid gap.<br />
Several shots were made with the modified Marx generator. In these experiments, the<br />
modified Marx generator connected directly with the five carbon-fiber cathodes.<br />
However, the emission was ceased in a very short time. Besides this limitation, the five<br />
cathodes could not be fired at the same time using the modified Marx generator, due to<br />
the non-uniformity of the cathode array. Therefore a special multi-beam pulse generator<br />
was built for the multi-beam carbon-fiber CRM array.<br />
72
Emitter voltage [kV]<br />
5<br />
3<br />
1<br />
-1<br />
-3<br />
-5<br />
0 200 400 600<br />
0<br />
800<br />
Time [us]<br />
Fig. 3.12. A typical cathode voltage and current traces without an accelerating voltage.<br />
Emitter voltage [kV] and<br />
accelerating voltage [kV]<br />
5<br />
3<br />
1<br />
-1<br />
-3<br />
-5<br />
Accelerating voltage<br />
Emitter Voltage<br />
0 200 400 600<br />
0<br />
800<br />
Time [us]<br />
Fig. 3.13. A typical cathode voltage and current traces with an accelerating voltage.<br />
73<br />
5<br />
4<br />
3<br />
2<br />
1<br />
5<br />
4<br />
3<br />
2<br />
1<br />
Collector current [A]<br />
Collector current [A]
A series of measurements were made with the different number of the cathodes in<br />
similar condition. The influence of the number of beams on the breakdown of the system<br />
was checked. A typical experimental result of the electron gun with a single cathode is<br />
shown in Fig. 3.14. Figs. 3.14 a, b, c, and d represent the emitter voltage for a one<br />
channel, the accelerating voltage, the current at the collector, and the current at the<br />
accelerating gap, respectively. The corresponding experimental measurement of the<br />
electron gun with the five-beam cathode array is shown in Fig. 3.15. In this case, the<br />
appearance of a breakdown at the accelerating stage depends on the array density. The<br />
diode voltage for each channel in the experiment of the five-beam cathode array is similar<br />
to the voltage in the experiment of the one-beam cathode array. In a similar diode voltage<br />
for each cathode, when the number of cathodes increases, the effective accelerating<br />
voltage, which does not cause the breakdown of the system, becomes lower (~7 kV in<br />
Fig. 3.14b and ~3 kV in Fig. 3.15b, i.e. ~4 kV difference). Decreasing the input energy for<br />
each cathode, Fig. 3.16 and Fig. 3.17 show the observed results for the electron gun with<br />
one-beam and three-beam cathode array, respectively. Again, when the number of<br />
cathodes increases, the effective accelerating voltage becomes lower (~11 kV in Fig.<br />
3.16b and Fig. 3.17b without and with breakdown, respectively). But here the difference<br />
is much smaller, perhaps because the distance between two cathodes in the three-beam<br />
array is two times wider than the distance in the five-beam array. Comparing Fig. 3.14<br />
and Fig. 3.16, we also found that the effective accelerating voltage decreases when the<br />
diode-input energy increases in the same number of beams (7 kV in Fig. 3.14b and 11 kV<br />
in Fig. 3.16b). Therefore, the effective accelerating voltage is inversely proportional to the<br />
current density. In our configuration, the effective accelerating voltage for the electron<br />
gun with the three-cathode array is more than 7 kV; whereas, for the electron gun with the<br />
five-cathode array, the effective accelerating voltage is much smaller, around 3 kV.<br />
These tests are important because this is the first exploration of electron guns with multi-<br />
beam cold cathodes. It demonstrates that the ~400 µs multi-pulse with ~0.1 A for each<br />
channel can be produced with this configuration. We found that in similar diode voltage<br />
for each cathode, when the number of cathodes is increased, a lower effective accelerating<br />
voltage can be achieved, and the achieved effective accelerating voltage is decreased<br />
when the diode-input energy is increased in the same number of the beams.<br />
74
Emitter voltage<br />
[kV]<br />
Accelerating<br />
voltage [kV]<br />
Collector current [A]<br />
Current at accelerating<br />
gap [A]<br />
4<br />
2<br />
0<br />
10<br />
5<br />
0<br />
2<br />
1<br />
0<br />
15<br />
10<br />
5<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0 200 400 600 800<br />
Time [us]<br />
Fig. 3.14. An experimental measurements for a single cathode gun:<br />
(a) the emitter voltage, (b) the accelerating voltage,<br />
(c) the collector current, and (d) the current at the accelerating stage.<br />
75
Emitter voltage<br />
[kV]<br />
Accelerating<br />
voltage [kV]<br />
Collector current<br />
[A]<br />
Current at<br />
accelerating gap [A]<br />
4<br />
2<br />
0<br />
6<br />
4<br />
2<br />
0<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0 200 400<br />
Time [us]<br />
600 800<br />
Fig. 3.15. An experimental measurements for a five-cathode gun:<br />
(b) the emitter voltage, (b) the accelerating voltage,<br />
(c) the collector current, and (d) the current at the accelerating stage.<br />
76
Emitter voltage [kV]<br />
Accelerating<br />
voltage [kV]<br />
Collector current [A]<br />
Current at accelerating<br />
gap [A]<br />
4<br />
2<br />
0<br />
15<br />
10<br />
5<br />
0<br />
2<br />
1<br />
0<br />
1<br />
0.5<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0 200 400<br />
Time [us]<br />
600 800<br />
Fig. 3.16. An experimental measurements for a single cathode gun with a<br />
decreased input voltage:<br />
(d) the emitter voltage, (b) the accelerating voltage,<br />
(c) the collector current, and (d) the current at the accelerating stage.<br />
77
Emitter voltage<br />
[kV]<br />
Accelerating<br />
voltage [kV]<br />
Collector current [A]<br />
Current at accelerating<br />
gap [A]<br />
4<br />
2<br />
0<br />
15<br />
10<br />
5<br />
0<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0 200 400 600 800<br />
Time [us]<br />
Fig. 3.17. An experimental measurements for a three-cathode gun:<br />
(c) the emitter voltage, (b) the accelerating voltage,<br />
(c) the collector current, and (d) the current at the accelerating stage.<br />
78
3.1.3. Magnetic Fields<br />
One of the major concerns about the multi-beam carbon-fiber CRM-array is the nonuniformity<br />
of the transverse contributions of the focusing magnetic field. A careful design<br />
of the solenoid was made to incorporate one main coil and two side coils. In this solenoid,<br />
the side coils were used to improve the uniformity near the edge of the magnetic field.<br />
Fig. 3.18 shows the cross section of the solenoid. The main coil was made out of a 2 mm<br />
diameter copper wire with 9.8 turns/cm. The two side coils were made out of a 2 mm<br />
diameter copper wire with 5 turns/cm. A large diameter kicker was designed in order to<br />
spin up the electrons. It was made out of a 1 mm diameter copper wire with 32 loops/cm.<br />
The final design of the kicker can be made in two ways. One method is to insert an array<br />
of thin, trim coils in the vacuum chamber, in order to produce the uniformity of transverse<br />
fields for each beam. The second method concerns the electrostatic effect. That means<br />
using the electrode structure to change the electrostatic field around cathodes. In the final<br />
off-axis design it may have a small difference in the electric field on the two sides of the<br />
electron beams. This could be designed by purposely inserting an asymmetric metal piece.<br />
The axial magnetic field at any point of the solenoid is calculated by Eq. 2.1. The<br />
result of the computer simulation is given in Fig. 3.19. In Fig. 3.19, the magnetic field of<br />
the main coil is shown by the dash-dot curve, the magnetic fields of the side coils are<br />
shown by the two small dashed curves, and the magnetic field of the solenoid is shown by<br />
the solid curve. The star sign represents the front position of the cathodes. In principle, the<br />
off-axis magnetic field of the solenoid can be calculated using the formulas or special<br />
software. In the experiment, a Gauss meter was used to check the magnetic field<br />
uniformity near the edge of the solenoid [114]. The parameters of the solenoid and the<br />
kicker are shown in Table 3.2.<br />
Fig. 3.18. Solenoid in cross section.<br />
79<br />
z<br />
B
Fig. 3.19. The magnetic field of the solenoid.<br />
Table 3.2. The parameters of the solenoid and the kicker.<br />
Parameter Main coil Side coil Kicker<br />
Turns 780 15 98<br />
Current [A] 100-200 100-200 20-140<br />
Inner radius [cm] 5.7 6.1 7<br />
Outer radius [cm] 6.1 6.3 7.4<br />
Length [cm] 80 3 3.5<br />
80
3.1.4. The Periodic Waveguide<br />
A photograph of the periodic waveguide is shown in Fig. 3.20. The waveguide<br />
consists of a metal-post array with 6x20 elements and is terminated by half-period<br />
reflecting sections in both ends. Figs. 3.21a and b show the measured resonant absorption<br />
and transmission peaks corresponding to the axial modes of the cavity at the first and<br />
second passbands, respectively. The resonances were measured by looking at the<br />
reflection coefficient (upper traces in Fig. 3.21 a, b) of the slow wave structure over the<br />
appropriate frequency range, as described in Section 2.1.4. The waveguide dispersion is<br />
shown in a Brillouin diagram in Fig. 3.22, as results from the measurements of the<br />
waveguide reflection and transmission coefficients. These intersections are shown by the<br />
dots in Fig. 3.22. The electron beam line is added to Fig. 3.22 in order to demonstrate<br />
CRM interaction in the first passband. The point a, which is the intersection of the<br />
electron beam line and the waveguide dispersion curves, indicates a possible CRM<br />
interaction with backward wave. Forward and backward wave interactions (β > 0 and<br />
n<br />
β n < 0 , respectively) differ by the tendency of the latter to act as absolute instabilities,<br />
and to oscillate (as observed in this experiment). The backward wave interaction could be<br />
the desired mode for a CRM-array oscillator. In amplifier schemes, however, parasite<br />
backward-wave interactions can be eliminated by a proper tuning to a tangential (grazing)<br />
point in Fig. 3.22.<br />
Fig. 3.20. Photograph of the periodic waveguide.<br />
81
(a)<br />
Fig. 3.21. The measured reflection and transmission curves at the<br />
first passband (a) and the second passband (b).<br />
82<br />
(b)
Frequency [GHz]<br />
10<br />
8<br />
6<br />
4<br />
2<br />
a<br />
-105 -64 -23 23 64 105<br />
Wave number [1/m]<br />
Fig. 3.22. The measured Brillouin diagram of the 2D periodic<br />
waveguide. The dashed line represents Eq. 1.1 in a<br />
cyclotron frequency at 6 GHz.<br />
83
3.2. Experimental Operation<br />
Each experiment began with a pre-running period to activate the cathodes. We found<br />
the following break-in procedure is useful. First, the cathode is under vacuum for several<br />
hours before firing them. Then, the operation is begun at the minimum voltage required to<br />
initiate the emission. After few tens of shots, the change of the gas pressure coursed by<br />
the cathode emissions should be reduced, compared with the first shots. Meanwhile, the<br />
accelerating voltage is increased in gradual until the desired voltage is achieved. In order<br />
to reduce the surface contamination, to stabilize the pressure and field emission currents,<br />
it is necessary to wait enough time between two shots.<br />
A control trigger system was used with function generators. The system connection is<br />
shown in Fig. 3.23. The main trigger comes from the solenoid pulser. Then it is sent to<br />
three function generators. After some delay, three trigger signals come out from the<br />
function generators and are sent to the gun pulser, kicker pulser and the 615 MR Pulserad<br />
control panel.<br />
Solenoid Pulser<br />
Trig.<br />
Gun Pulser<br />
Trig. Trig. TTL output<br />
Kicker Pulser<br />
Trig. Trig. TTL output<br />
Control panel of<br />
Function generator<br />
615 MR Pulserad<br />
EXT. Trig. Trig. TTL output<br />
Fig. 3.23. The trigger system.<br />
84<br />
Function generator<br />
Function generator
3.3. Experimental Results<br />
A typical experimental result of the three-beam carbon-fiber CRM-array is shown in<br />
Fig. 3.24. The emitter voltage of the center carbon-fiber cathode is shown in Fig. 3.24a.<br />
The accelerating voltage is shown in Fig. 3.24b. The cathode input current, measured by a<br />
Rogowsky coil, is shown in Fig. 3.24c. The microwave radiation output, detected through<br />
a 4.7-5.3 GHz bandpass filter, is shown in Fig. 3.24d. The axial magnetic field in this run<br />
is 2.4 kG, which corresponds to a cyclotron frequency of 6.8 GHz, hence the device<br />
operates in the backward-wave regime.<br />
Another radiation burst, observed with a similar magnetic field in the three-beam<br />
carbon-fiber CRM-array, is shown in Fig. 3.25. The emitter voltage of the center channel<br />
carbon-fiber cathode is shown in Fig. 3.25a. The accelerating voltage and the detector<br />
output are shown in Fig. 3.25b and Fig. 3.25c, respectively. A slightly higher electron<br />
energy (~8kV accelerating voltage) results in a three-peak shape of the detector output, as<br />
shown in Fig. 3.26c.The burst in center did not pass a 4.7-5.3 GHz bandpass filter and it<br />
may be caused by noises. However, the two side peaks of the signal passed through the<br />
4.7-5.3 GHz bandpass filter.<br />
Fig. 3.27 shows a typical case observed in the experiment. After the radiation burst is<br />
detected, a breakdown occurs at the accelerating stage. Fig. 3.27d shows the breakdown<br />
current. A series of measurements were made in similar conditions with three electron<br />
beams. The output power in the receiving antenna attains ~5 W.<br />
The multi-beam cold-cathode CRM-array was also operated with five carbon-fiber<br />
cathodes. Bursts were observed as shown in Fig. 3.28 and Fig 3.29. However, these bursts<br />
could not pass the 4.7-5.3 GHz band pass filter. Meanwhile, we observed the breakdown<br />
current, which started at the same time with the bursts at the accelerating stage. Therefore,<br />
these bursts may be caused by the breakdown and they are not the same as those in Fig.<br />
3.27.<br />
85
Accelerating<br />
voltage [kV]<br />
Current [A]<br />
RF detector<br />
output [V]<br />
Cathode voltage [kV]<br />
10<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0.1<br />
0.08<br />
0.06<br />
0.04<br />
0.02<br />
0<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
8<br />
6<br />
4<br />
2<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0 100 200 300 400 500 600<br />
Time [us]<br />
Fig. 3.24. Typical experimental measurements for a three-beam CRM at 2.4 kG:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the cathode input current, (d) the RF detector output.<br />
86
Detector voltage [mV]<br />
Cathode voltage [kV]<br />
Accelerating voltage [kV]<br />
100<br />
80<br />
60<br />
40<br />
20<br />
8<br />
6<br />
4<br />
2<br />
(a)<br />
0<br />
120 160 200 240 280 320 360<br />
Time [us]<br />
8<br />
6<br />
4<br />
2<br />
(b)<br />
0<br />
120 160 200 240 280 320 360<br />
Time [us]<br />
(c)<br />
0<br />
120 160 200 240 280 320 360<br />
Time [us]<br />
Fig. 3.25. An experimental measurements for a three-beam CRM:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the RF detector output.<br />
87<br />
400<br />
400<br />
400<br />
400
Cathode voltage [kV]<br />
Accelerative voltage<br />
[kV]<br />
Detector output [V]<br />
4<br />
3<br />
2<br />
1<br />
0<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
(a)<br />
190 230 270 310 350 390<br />
Time [us]<br />
(b)<br />
190 230 270 310 350 390<br />
Time [us]<br />
(c)<br />
190 230 270 310 350 390<br />
Time [us]<br />
Fig. 3.26. An experimental measurements for a three-beam CRM:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the RF detector output.<br />
88
Accelerating voltage<br />
[kV]<br />
Detector output [V]<br />
Cathode voltage [kV]<br />
Current at accelerating<br />
stage [A]<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0.50<br />
0.40<br />
0.30<br />
0.20<br />
0.10<br />
0.00<br />
8<br />
6<br />
4<br />
2<br />
4<br />
3<br />
2<br />
1<br />
0<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
0<br />
100 200 300 400<br />
Time [us]<br />
Fig. 3.27. An experimental measurements for a three-beam CRM:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the RF detector output, (d) the current breakdown at accelerating stage.<br />
89
Detector output [V]<br />
Cathode voltage [kV]<br />
4<br />
3<br />
2<br />
1<br />
0<br />
Accelerating voltage<br />
[kV]<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
6<br />
4<br />
2<br />
0<br />
(a)<br />
80 120 160 200<br />
Time [us]<br />
(b)<br />
80 120 160 200<br />
(c)<br />
Time [us]<br />
80 120 160 200<br />
Time [us]<br />
Fig. 3.28. An experimental measurements for a five-beam CRM at 2.1 kG:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the RF detector output.<br />
90
Detector output [V]<br />
Cathode voltage [kV]<br />
Accelerating voltage [kV]<br />
4<br />
2<br />
0<br />
4<br />
2<br />
0<br />
0.80<br />
0.60<br />
0.40<br />
0.20<br />
0.00<br />
(a)<br />
80 120 160 200<br />
Time [us]<br />
(b)<br />
80 120 160 200<br />
Time [us]<br />
(c)<br />
80 120 160 200<br />
Time [us]<br />
Fig. 3.29. An experimental measurements for a five-beam CRM at 2.1 kG:<br />
(a) the carbon-fiber cathode voltage, (b) the accelerating voltage,<br />
(c) the RF detector output.<br />
91
3.4. Discussions<br />
Considerable progress has been made during this experiment. However, there were<br />
some difficulties with the multi-beam cold-cathode CRM-array. Beside the similar<br />
difficulties with the thermionic cathode CRM arrays we discussed in Chapter 2, the<br />
uniformity of the emission current was a major issue to deal with in the experiments.<br />
Since the field-emitted current is extremely sensitive to the value of the field at the emitter<br />
tip, and small changes in the anode-cathode separation could lead to large difference in<br />
emitted current for each cathode. In the beginning, we used single channel pulse generator<br />
to drive the multi-beam carbon-fiber cathode array. Although we tried to maintain<br />
parallelism between the anode and the separate cathodes, it was hard to get a uniform<br />
emission current since poor accuracy by this manufacture method. No matter how many<br />
times we changed the grid voltage, anode voltage, and adjusted the high resistive blaster<br />
resistor for each channel, we could not get five emission electron beams simultaneously<br />
for the most of shoots. Finally we built a five-channel pulse generator which has five<br />
separate output high voltage channels but with the same trigger system. By using this<br />
generator the uniformity was improved successfully.<br />
Another issue was the vacuum breakdown. As described in Section 3.1.2.4, the relative<br />
long rise time of the high voltage pulse caused the carbon fibers flare on a critical voltage.<br />
Since the high voltage (> 3kV) is necessary for CRM interactions, we need a high<br />
accelerating voltage between the grid and the anode. However, there was always<br />
breakdown when we add a large accelerating voltage at the beginning. During these CRM<br />
experiments, we used the break-in operating process for the multi-beam cold-cathode<br />
array. The process of operation consists of the following steps. First the accelerating<br />
voltage should be increased in gradual, then waiting enough time at each shot in order to<br />
reduce the surface contamination, to stabilize the pressure and field emission currents.<br />
This time is longer when the number of beams is increased in these experiments.<br />
Complying with this process, we have reached 7 kV accelerating voltage in the threebeam<br />
carbon-fiber CRM experiment.<br />
92
The theoretical tuning condition of the CRM interaction (Eq. 1.1) and the Brillouin<br />
dispersion diagram of Fig. 3.22 were applied to analyze the three-beam carbon-fiber CRM<br />
experimental results. The CRM tuning condition indicates clearly that these interactions<br />
occurred with backward waves.<br />
Although we have successfully explored the multi-beam cold-cathode array in the<br />
experiment, some improvements need to be done in future. First, the cathodes for this<br />
research are fabricated in a very simply way. It will improve the performance if a Spindt<br />
type cathode would be used (a possible vendor offering this semiconductor process<br />
technology is NEC Corporation in Japan or MCNC in US [115]). Second, it is necessary<br />
to use relatively short pulse generators in order to prevent the breakdown, improve the<br />
flatness of the emitted current and increase the repetition rate. Third, some improvement<br />
in material, such as coating with Cesium iodide (CsI), may also helpful [103,104].<br />
The experiments of the carbon-fiber CRM arrays have clearly demonstrated the<br />
principle of the multi-beam CRM scheme with the cold-cathode array, and explored the<br />
use of a multi-beam cold-cathode array in vacuum electronic devices. The multi-beam<br />
cold-cathode array which is based on commercial carbon fibers was used as an electron<br />
source and produced a multi-channel ~400 µs long pulse. In the carbon-fiber CRM-array<br />
experiments, the three-beam CRM-array operated at low voltages, around 5kV, with a<br />
~0.4 ms pulse duration. Clear bursts of RF oscillations were observed around 5 GHz in<br />
this experiment. These experimental results show that it could be possible to use coldcathode<br />
arrays in multi-beam CRM devices in the near future.<br />
93
Chapter 4<br />
Conclusions<br />
The major objective of this study was to demonstrate, for the first time, a multi-beam<br />
CRM-array operation, and to study its features experimentally. The significance of the<br />
research is the experimental verification of the CRM-array conceptual feasibility, as a<br />
stage toward larger multi-beam CRM arrays. In addition, a secondary objective of this<br />
research was to explore the multi-beam CRM device using cold-cathode arrays and to<br />
develop an efficient, reliable and cost-effective multi-beam electron source.<br />
4.1. Experimental Results<br />
In the experimental study with thermionic cathodes, CRM oscillators were operated in<br />
a 2D scheme with one and two low-energy electron-beams (
Clear bursts of RF oscillations are observed around 5 GHz in the experiment. The<br />
experimental results show that it is might possible to use cold-cathode arrays in multibeam<br />
CRM devices in the near future.<br />
4.2 Suggestions for Future Work<br />
These experiments provided a preliminary investigation of the multi-beam CRM-array,<br />
and a good starting point for future experimental studies of large-scale multi-beam CRM<br />
arrays, and multi-beam cold-cathode arrays. The next challenge is probably to improve the<br />
RF output power of the multi-beam CRM devices. The implementation of this goal<br />
requires a careful design of the electron guns, and of the microwave components<br />
(preferably by advanced 3D codes). A full numerical simulation of the CRM array is<br />
essential, not only for a proper design but also for the analysis and optimization of the<br />
experimental results.<br />
Further experiments on larger arrays with a repetitive pulsed operation would be<br />
useful. The immediate repetitive operation for 2D CRM-array with thermionic cathodes<br />
can be designed and constructed. However, future improvement of RF power and<br />
operation with carbon-fiber CRM arrays will need relatively short pulse generators in<br />
order to prevent the breakdown, improve the flatness of emission current and increase<br />
repetitive rate. A potential limitation on the repetition rate with a carbon-fiber cathode<br />
array is the time required for the plasma to clear out of the gap. This time seems to be<br />
longer in these experiments when the number of beams is increased. It will improve the<br />
performance if Spindt type cathodes were used. A good processing for the carbon fibers<br />
will be also helpful since the material coating can reduce the closure speed. In order to<br />
decrease the closure speed, some improvement in material, such as coating with Cesium<br />
iodide (CsI), may be helpful.<br />
A consequent 3D CRM-array experiment that employs a 3×3 thermionic cathode array<br />
is under construction and operation in our research group by other researchers, and studies<br />
of direct radiation from CRM arrays, active phased-array antenna features, and radiation<br />
steering will be carried out in foreseeable future.<br />
95
Appendix A<br />
Computer Programs and Simulations Documentation<br />
A1. The EGUN Code Simulation for the 2D CRM-array Experiment<br />
The electron gun design was performed with the EGUN code [108] in the 2D CRMarray<br />
experiment. The boundary used to model the electron gun which has a 5mm<br />
diameter cathode and 6 mm gap is shown in Table A1 and Fig. A1. The potential 1<br />
represents the cathode and the potential 2 represents the anode.<br />
Table A1. The data of the geometry.<br />
Potential 1 1 0 0 3 3 0 0 2 2 2 2 0 1<br />
X 0 2.5 2.5 25 25 25 25 25 25 3 3 0 0 0<br />
Y 0 0 0 0 0 1 1 6 6 6 40 40 40 0<br />
Potential 3<br />
Potential 1<br />
2.5 mm<br />
X<br />
6 mm<br />
Potential 2<br />
40 mm<br />
Fig. A1. The geometry used to model the e-gun in the 2D CRM-array<br />
experiment with a 5mm diameter cathode.<br />
96<br />
25 mm<br />
3 mm<br />
Y
The Data of File<br />
The EGUN code output for a 5mm cathode and 6mm gap (B~2.2 kG) in Fig. 2.4.<br />
&INPUT1 RLIM = 25, ZLIM = 40, NBND = 320, POTN = 3,<br />
POT( 1) = 1.0000E-01,<br />
POT( 2) = 7.0000E+03,<br />
POT( 3) = 1.0000E-01,<br />
MAGSEG = 0, IAX = 0, AQUAD = 0.0, CSYS = 1,<br />
MI = 3, SX = 7.50, SY = 4.69, SCALE =' ',<br />
PASS = 2, XR =0.9950, ERROR =0.1000E-02, TYME= 300.0,<br />
LSTPOT = 3, LSTMAG = 1, LSTBND = 1, INTPA = 0, POIS = 0, &END<br />
1 0 1 0.0000000 -0.9990000<br />
1 1 1 2.0000000 -0.9990000<br />
1 2 1 2.0000000 -0.9990000<br />
1 3 0 -0.4980896 0.0000000<br />
0 4 0 2.0000000 0.0000000<br />
0 22 0 2.0000000 0.0000000<br />
0 23 0 2.0000000 0.0000000<br />
3 24 0 0.9990000 0.0000000<br />
3 24 1 0.9990000 2.0000000<br />
3 24 2 0.0000000 -0.9990000<br />
0 24 3 0.0000000 2.0000000<br />
0 24 4 0.0000000 2.0000000<br />
0 24 5 0.0000000 2.0000000<br />
2 24 6 0.0000000 0.0010000<br />
2 23 6 2.0000000 0.0010000<br />
2 5 6 2.0000000 0.0010000<br />
2 4 6 2.0000000 0.0010000<br />
2 3 7 0.0010000 2.0000000<br />
2 3 38 0.0010000 2.0000000<br />
2 3 39 0.0010000 2.0000000<br />
97
2 3 40 0.0010000 0.0052147<br />
2 2 40 2.0000000 0.0052490<br />
2 1 40 2.0000000 0.0052795<br />
2 0 40 0.0000000 0.0053139<br />
0 0 39 0.0000000 2.0000000<br />
0 0 4 0.0000000 2.0000000<br />
0 0 3 0.0000000 2.0000000<br />
0 0 2 0.0000000 2.0000000<br />
888<br />
&INPUT5 START ='SPHERE', RMAX = 2.500, RAD = 0.2500E+05, MAXRAY =<br />
20,<br />
LSTRH = 1,UNIT =0.1000E-02<br />
NMAG=20,<br />
CR=35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,<br />
CZ=0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,<br />
CM=3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,30<br />
00,3000,3000,3000,3000,3000,<br />
&END<br />
98
A2. The Magnetic Fields Calculation for the 2D CRM-array Experiment<br />
The magnetic field at the 2D CRM-array experiment is caculated by Eq.2.1 [109].<br />
The Matlab program follows:<br />
% Fig2-6mag.m<br />
% Magnetic field calculation for solenoid and kicker in the 2D multi-beam array<br />
experiment<br />
z=-0.2:5e-5:.8; %step<br />
u=4*pi*1e-7; %constant<br />
N1=120;N2=225*4; %turns<br />
Ik1=20*3.2;Ik2=20*7.16; %current<br />
r2=.065;r4=0.103/2; %Solenoid & Kicker parameters (inner diameter)<br />
r1=.055;r3=0.126/2; %Solenoid & Kicker parameters (outner diameter)<br />
l1=0.023;l2=.6; %length<br />
z2=-0.07/2+0.01-0.3; %shift<br />
z1=-0.09;<br />
%MAGNETIC FIELD (Kicker)<br />
Bk1=u*N1*Ik1/2/(r2-r1)/l1*((z+z1+l1/2).*log((r2+sqrt(r2^2+(z+z1+l1/2).^2))./ .....<br />
(r1+sqrt(r1^2+(z+z1+l1/2).^2)))-(z+z1-l1/2).*log((r2+sqrt(r2^2+(z+z1-l1/2).^2))./ ....<br />
(r1+sqrt(r1^2+(z+z1-l1/2).^2))));<br />
%MAGNETIC FIELD (Solenoid)<br />
Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log ......<br />
((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ .....<br />
(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log .....<br />
((r4+sqrt(r4^2+((z+z2)-l2/2).^2))./ ....<br />
(r3+sqrt(r3^2+((z+z2)-l2/2).^2))));<br />
99
hold on<br />
plot(z,Bs,'b')<br />
hold on<br />
plot(z,Bk1,'r--')<br />
hold on<br />
title('Magnetic field=f(z)')<br />
xlabel('z (m)'),ylabel('B (tesla)')<br />
grid<br />
100
A3. The EGUN Code Simulation for the Carbon-fiber CRM-array<br />
Experiment<br />
The electron gun design was performed with the EGUN code [108] in the carbon-fiber<br />
CRM-array experiment. The boundary used to model the electron gun which has a 3mm<br />
diameter is shown in Table A2 and Fig. A2. The potential 1 represents the cathode, the<br />
potential 2 represents the grid, and the potential 4 represents the anode.<br />
Table A2. The Data of the Geometry.<br />
Potential 1 1 0 0 3 3 0 0 2 2 2 2 0 0 4 4 4 4 4 4 0 1<br />
X 0 1.5 1.5 25 25 25 25 25 25 3 3 25 25 25 25 3 3 25 25 0 0 0<br />
Y 0 0 0 0 0 1 1 8 8 8 9 9 9 19 19 19 21 21 40 40 40 0<br />
Potential 3<br />
Potential 2<br />
Potential 1<br />
1.5 mm<br />
X<br />
8 mm<br />
10 mm<br />
40 mm<br />
Fig. A2. The geometry used to model the e-gun in the carbon-fiber<br />
CRM-array experiment with a 3mm diameter cathode.<br />
101<br />
Potential 4<br />
25 mm<br />
3 mm<br />
Y
The Data of File<br />
The Hermannsfedt code output for a 3 mm carbon-fiber cathode in Fig. 3.7.<br />
&INPUT1 RLIM = 25, ZLIM = 40, NBND = 320, POTN = 4,<br />
POT( 1) = 1.0000E-01,<br />
POT( 2) = 4.0000E+03,<br />
POT( 3) = 1.0000E-01,<br />
POT( 4) = 12.0000E+03,<br />
MAGSEG = 0, IAX = 0, AQUAD = 0.0, CSYS = 1,<br />
MI = 3, SX = 7.50, SY = 4.69, SCALE =' ',<br />
PASS = 2, XR =0.9950, ERROR =0.1000E-02, TYME= 300.0,<br />
LSTPOT = 3, LSTMAG = 1, LSTBND = 1, INTPA = 0, POIS = 0, &END<br />
1 0 1 0.0000000 -0.9990000<br />
1 1 1 2.0000000 -0.9990000<br />
1 2 1 2.0000000 -0.9990000<br />
1 3 0 -0.9990000 0.0000000<br />
0 4 0 2.0000000 0.0000000<br />
0 22 0 2.0000000 0.0000000<br />
0 23 0 2.0000000 0.0000000<br />
3 24 0 0.9990000 0.0000000<br />
3 24 1 0.9990000 2.0000000<br />
3 24 2 0.0000000 -0.9990000<br />
0 24 3 0.0000000 2.0000000<br />
0 24 6 0.0000000 2.0000000<br />
0 24 7 0.0000000 2.0000000<br />
2 24 8 0.0000000 0.0010529<br />
2 23 8 2.0000000 0.0010529<br />
2 5 8 2.0000000 0.0010529<br />
2 4 8 2.0000000 0.0010529<br />
2 3 9 0.0010000 2.0000000<br />
2 4 10 2.0000000 -0.9990000<br />
102
2 22 10 2.0000000 -0.9990000<br />
2 23 10 2.0000000 -0.9990000<br />
2 24 10 0.0000000 -0.9990000<br />
0 24 11 0.0000000 2.0000000<br />
0 24 17 0.0000000 2.0000000<br />
0 24 18 0.0000000 2.0000000<br />
4 24 19 0.0000000 0.0024853<br />
4 23 19 2.0000000 0.0024853<br />
4 5 19 2.0000000 0.0024853<br />
4 4 19 2.0000000 0.0024853<br />
4 3 20 0.0010000 2.0000000<br />
4 3 21 0.0010000 2.0000000<br />
4 4 22 2.0000000 -0.9990000<br />
4 22 22 2.0000000 -0.9990000<br />
4 23 22 2.0000000 -0.9990000<br />
4 24 22 0.9990000 -0.9990000<br />
4 24 23 0.9990000 2.0000000<br />
4 24 38 0.9990000 2.0000000<br />
4 24 39 0.9990000 2.0000000<br />
4 24 40 0.9990000 0.0052185<br />
4 23 40 2.0000000 0.0052223<br />
4 22 40 2.0000000 0.0052261<br />
4 21 40 2.0000000 0.0052299<br />
4 20 40 2.0000000 0.0052338<br />
4 19 40 2.0000000 0.0052376<br />
4 18 40 2.0000000 0.0052414<br />
4 17 40 2.0000000 0.0052452<br />
4 16 40 2.0000000 0.0052490<br />
4 15 40 2.0000000 0.0052528<br />
4 14 40 2.0000000 0.0052567<br />
4 13 40 2.0000000 0.0052605<br />
103
4 12 40 2.0000000 0.0052681<br />
4 11 40 2.0000000 0.0052719<br />
4 10 40 2.0000000 0.0052757<br />
4 9 40 2.0000000 0.0052795<br />
4 8 40 2.0000000 0.0052834<br />
4 7 40 2.0000000 0.0052872<br />
4 6 40 2.0000000 0.0052910<br />
4 5 40 2.0000000 0.0052948<br />
4 4 40 2.0000000 0.0052986<br />
4 3 40 2.0000000 0.0053024<br />
4 2 40 2.0000000 0.0053062<br />
4 1 40 2.0000000 0.0053101<br />
4 0 40 0.0000000 0.0053139<br />
0 0 39 0.0000000 2.0000000<br />
0 0 4 0.0000000 2.0000000<br />
0 0 3 0.0000000 2.0000000<br />
0 0 2 0.0000000 2.0000000<br />
888<br />
&INPUT5 START ='SPHERE', RMAX = 2.000, RAD = 0.2000E+05, MAXRAY =<br />
-20,<br />
LSTRH = 1,UNIT =0.1000E-02<br />
NMAG=20,<br />
CR=50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,<br />
CZ=-20,-10,0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,<br />
CM=1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,15<br />
00,1500,1500,1500,1500,1500,<br />
&END<br />
104
A4. The Magnetic Fields Calculation for the Carbon-fiber CRM-array<br />
Experiment<br />
The magnetic field at the Carbon-fiber CRM-array experiment is caculated by Eq.2.1<br />
[109]. It is a little different with Section A2, since the solenoid consists of three coils. The<br />
Matlab program is as follows:<br />
whitebg<br />
clc<br />
clear<br />
hold off<br />
% Magnetic field of 5-beam CRM-array<br />
z=-0.1:5e-5:.9;<br />
u=4*pi*1e-7; %air permability<br />
%Solenoid & Kicker parameters<br />
N1=15;N2=390*2;N3=15; %turns<br />
Ik1=20*8.24;Ik2=20*8.24;Ik3=20*8.24; %currents<br />
r2=.1265/2;r4=0.1225/2;r6=0.1265/2; %external radius<br />
r1=.1225/2;r3=0.1143/2;r5=0.1225/2; %inner radius<br />
l1=0.03;l2=.8;l3=0.03; %length<br />
z1=-(0.028+0.015); %center of sidecoil1<br />
z2=-0.4; %center of solenoid<br />
z3=-(0.8-0.028-0.015); %center of sidecoil2<br />
%MAGNETIC FIELD (side coil1)<br />
Bk1=u*N1*Ik1/2/(r2-r1)/l1*((z+z1+l1/2).*log((r2+sqrt(r2^2+(z+z1+l1/2).^2))./ .....<br />
(r1+sqrt(r1^2+(z+z1+l1/2).^2)))-(z+z1-l1/2).*log((r2+sqrt(r2^2+(z+z1-l1/2).^2))./ ....<br />
(r1+sqrt(r1^2+(z+z1-l1/2).^2))));<br />
%MAGNETIC FIELD (side coil2)<br />
Bk3=u*N3*Ik3/2/(r6-r5)/l3*((z+z3+l3/2).*log((r6+sqrt(r6^2+(z+z3+l3/2).^2))./ .....<br />
(r5+sqrt(r5^2+(z+z3+l3/2).^2)))-(z+z3-l3/2).*log((r6+sqrt(r6^2+(z+z3-l3/2).^2))./ ....<br />
(r5+sqrt(r5^2+(z+z3-l3/2).^2))));<br />
105
%MAGNETIC FIELD (Solenoid)<br />
Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ .....<br />
(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log((r4+sqrt(r4^2+((z+z2)l2/2).^2))./<br />
....<br />
(r3+sqrt(r3^2+((z+z2)-l2/2).^2))));<br />
B=Bk1+Bs+Bk3;<br />
plot(z,B,'k')<br />
hold on<br />
plot(z,Bs,'k-.')<br />
hold on<br />
plot(z,Bk1,'k--')<br />
hold on<br />
plot(z,Bk3,'k--')<br />
hold on<br />
title('Mag.field=f(z)')<br />
xlabel('z (m)'),ylabel('B (tesla)')<br />
grid<br />
z=0.04;<br />
%MAGNETIC FIELD (side coil1)<br />
Bk1=u*N1*Ik1/2/(r2-r1)/l1*((z+z1+l1/2).*log((r2+sqrt(r2^2+(z+z1+l1/2).^2))./ .....<br />
(r1+sqrt(r1^2+(z+z1+l1/2).^2)))-(z+z1-l1/2).*log((r2+sqrt(r2^2+(z+z1-l1/2).^2))./ ....<br />
(r1+sqrt(r1^2+(z+z1-l1/2).^2))));<br />
%MAGNETIC FIELD (side coil2)<br />
Bk3=u*N3*Ik3/2/(r6-r5)/l3*((z+z3+l3/2).*log((r6+sqrt(r6^2+(z+z3+l3/2).^2))./ .....<br />
(r5+sqrt(r5^2+(z+z3+l3/2).^2)))-(z+z3-l3/2).*log((r6+sqrt(r6^2+(z+z3-l3/2).^2))./ ....<br />
(r5+sqrt(r5^2+(z+z3-l3/2).^2))));<br />
%MAGNETIC FIELD (Solenoid) `shifted .25`<br />
Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log ......<br />
((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ .....<br />
106
(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log .....<br />
((r4+sqrt(r4^2+((z+z2)-l2/2).^2))./ ....<br />
(r3+sqrt(r3^2+((z+z2)-l2/2).^2))));<br />
bb=Bk1+Bs+Bk3 ;<br />
plot(z,bb,'r*') %<br />
set(gca,'XLim',[-0.1 0.9])%<br />
set(gca,'yLim',[0 0.25])%<br />
107
Appendix B<br />
Circuits of the Pulsed Power Devices<br />
Fig. B1. Circuit of the gun-solenoid pulser.<br />
108
Fig. B2. Circuit of the kicker pulser.<br />
109
Fig. B3. Circuit of the multi-channel gun pulser.<br />
110
C1. Model 615 MR Pulserad<br />
Appendix C<br />
The Modified Marx Generator<br />
The Model 615 MR Pulserad is an electron-accelerator system designed specifically<br />
for high-power magnetron experiments by Physics International Company. It consists of<br />
five subassemblies: (1) a DC power supply and controls, (2) trigger amplifiers, (3) a Marx<br />
generator, (4) a pulse clipping switch (crowbar), and (5) a high-voltage vacuum bushing<br />
(diode) [116].<br />
Two trigger amplifiers mounted outside the pulser tank provide the high-level signals<br />
required to trigger the Marx generator and the crowbar switch. The trigger systems are<br />
comprised of a PT-70 control panel and a PT-55 trigger amplifier.<br />
Two inputs are required for these trigger operations: (1) a 7 kV DC bias and (2) a<br />
positive 300 V trigger. These inputs are supplied at the control console. The output of the<br />
trigger amplifier is a positive 50 kV pulse with a risetime of ≤ 10 ns and a duration of<br />
about 50 ns.<br />
External synchronization can be applied to the control function panel but must meet<br />
the following requirements: (1) ≥ +10 V, (2) ≤ 10 ns risetime, and (3) a pulse width of 50<br />
to 100 ns.<br />
The Pulserad 615 MR Marx generator consists of 6 energy storage "stages". In<br />
addition to a 0.5 µF high voltage capacitor, each stage also consists of some resistors and<br />
a spark gap which is pressurized with SF6. All the capacitors in the circuit are charged in<br />
parallel by the high voltage DC power supply. When the capacitors have been charged to<br />
the desired voltage level, the first stage is triggered by PT-55 trigger amplifier. This<br />
trigger pulse, which must exceed the breakdown strength (as low as 3 kV/mm) of the<br />
111
Marx gas in use (typically Nitrogen), causes the dielectric gas in the first stage to<br />
breakdown and become ionized (and thereby conducting). This effect causes the potential<br />
across the second stage gap to be twice the charging voltage. When all the spark gaps<br />
breakdown, the capacitors become connected in series across the load. Each capacitor is<br />
shunted by isolation resistors. Ignoring the losses in the isolation resistors and series<br />
resistive drops, the output voltage of the generator is six times of the DC charging<br />
voltage. A 12.5 Ω series-damping resistor is placed between the Marx and the diode to<br />
minimize reversal when the crowbar switch is fired.<br />
C2. The Modified Model 615 Pulserad<br />
The modified Pulserad 615 MR Marx generator is composed of capacitors, spark<br />
gaps, and resistors electrically arranged as shown in Fig. C1. Since we need a moderate<br />
voltage (< 20 kV) and long duration pulse in the experiment, we use the capacitor bank to<br />
supply the high voltage without the energy storage "stages". A spark gap is used as a fast<br />
speed switch. A 1 kΩ series resistor is placed between the spark gap and output in order<br />
to protect the capacitors.<br />
CRM<br />
system<br />
1 kΩ<br />
1 µF<br />
50 kV pulse<br />
1.5 kΩ<br />
20 kV High DC<br />
voltage supply<br />
112<br />
PT-55<br />
Trigger amplifier<br />
Fig. C1. The modified circuit in Model 615 MR Pulserad.<br />
Control<br />
function<br />
panel
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